JavaScript (ES6), 73 72 64 63 54 42 39 bytes

Thanks to Neil for saving 13 bytes

a=>a.map(b=>b.split` `.length)=='5,7,5'

Explanation

This is a fat-arrow function that takes an array of strings as argument. It replaces each line by its word count. If it is a haiku-w, a now contains an array of a five, a seven and a five again. Since JavaScript doesn't allow us to compare 2 arrays at the same time, the array is converted to a string first, and then compared. This results in a boolean that is returned.

Mathematica, 21 bytes

{4,6,4}==Count@" "/@#&

Unnamed function taking a list of lists of characters as input and returning True or False. Simply counts how many spaces are in each list of characters, which under the rules of the challenge correlate perfectly with the number of words in each line.

Previous submission:

Mathematica, 31 bytes

Length/@StringSplit/@#=={5,7,5}&

Unnamed function taking a list of strings as input and returning True or False.

Jelly, 10 9 bytes

ċ€⁶⁼“¥©¥‘

Try it online!

Explanation

ċ€⁶⁼“¥©¥‘  Input: length-3 list of strings
 €         For each string
ċ ⁶          Count the number of spaces
    “¥©¥‘  Convert string to code page indices, makes [4, 6, 4]
   ⁼       Match

Python, 42 bytes

lambda l:[s.count(' ')for s in l]==[4,6,4]

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Takes input as a list of lines, with the words separated by single spaces.

As we're guaranteed there'll be no leading or trailing spaces, and only single spaces will seperate each word, we can verify a w-haiku by simply counting the spaces in each line.

We do this in a list comprehension, to create a list of the space-counts. If it is a correct haiku, it should look like [4, 6, 4], so we compare it with this and return the result.

Batch, 102 bytes

@echo off
call:c&&call:c 2||exit/b
:c
set/an=%1+5
set/ps=
for %%W in (%s%)do set/an-=1
exit/b%n%

Exits with non-zero errorlevel as soon as it reads a line with the wrong number of words.

Perl, 26 bytes

24 bytes of code + 2 bytes for -ap flags.

$m.=@F}{$_=$m==575&$.==3

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Haskell, 34 33 bytes

f l=[sum[1|' '<-c]|c<-l]==[4,6,4]

Try it online!.

Edit: thanks to @xnor for a byte!

AWK (GNU Awk), 24, 30, 28, 20 bytes

Golfed

517253==$0=q=q NF NR

Will output "517253" for True, and empty string for False.

In awk, any nonzero numeric value or any nonempty string value is true. Any other value (zero or the null string, "") is false

The GNU Awk User's Guide

How It Works

Each awk statement (rule) consists of a pattern (or expression) with an associated action:

pattern {action}

Awk will read the input line by line (record by record) and evaluate pattern expression to see if a corresponding action is to be invoked.

The code above is a standalone Awk expression (pattern) w/o the action block, which is implied to be {print $0} in that case.

It should be read right-to-left:

q=q NF NR

Append a Number of Fields (words) and Number of Records (i.e. the current line number), to the variable q.

This way, when processing a proper Haiku-w, q will be set to:

• 51 - on line #1 (5 words)
• 5172 - on line #2 (5 words + 7 words)
• 517253 - on line #3 (5 words + 7 words + 5 words)

$0=q

Assign the newly computed value of q to $0 (which holds the whole current line/record by default).

517253==$0

Compare it with a "signature" for a proper Haiku-w (517253), if there is a match, the whole expression evaluates to "true" and a corresponding action (implicit print $0) is run, sending "517253" to stdout (True), otherwise output will be empty (False).

Note that this will properly recognize a Haiku-w, even if it is followed by an arbitrary number of garbage lines, but I believe that is ok, as:

A length-3 list of strings as an input is also acceptable.

(i.e. we can assume the input to be 3 lines long)

Test

>awk '517253==$0=q=q NF NR'<<EOF
The man in the suit
is the same man from the store.
He is a cool guy.
EOF

517253

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Python, 58 44 bytes

lambda h:[len(l.split())for l in h]==[5,7,5]

-14 by tbodt

Retina, 12 bytes

M%` 
^4¶6¶4$

(there's a trailing space after the first line)

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• M%`  - Count the number of spaces in each line.
• ^4¶6¶4$ - There should be 4, 6, and 4 spaces, and exactly three lines.

Prints 1 for valid input, 0 for invalid.

C 142 bytes

void f(){char *c;l=3;s[3]={0};while(l>0){if(*c==' ')s[l-1]++;if((*c=getchar())=='\n'){l--;}}printf("%d",(s[0]==4 && s[1]==6 && s[2]==4)?1:0);}

Ungolfed version:

void f()
{
  char *c;
  c = (char *)malloc(sizeof(char)); 
  int l=3;
  int s[3]= {0};


 while(l>0)
 {  
   if(*c==' ')
   s[l-1]++;

   if( (*c=getchar())=='\n')
   {    
     l--;        
   }   
 }
printf("%d",(s[0]==4 && s[1]==6 && s[2]==4)?1:0);

}

Returns 1 for 5/7/5 sequence else 1.

A positive testcase:

Pyth, 9 bytes

qj464T/R;

A program that takes input of a list of "quoted strings" and prints True or False as appropriate.

Test suite

How it works

qj464T/R;   Program. Input: Q
qj464T/R;Q  Implicit variable fill
     T      Are the base-10
 j          digits
  464       of 464
q           equal
      /     to the number
        ;   of spaces
       R    in each string
         Q  in the input?
            Implicitly print

Pyke, 11 9 bytes

dL/uq

Try it here!

dL/       -  map(i.count(" "), input)
        q - ^ == V
   u  -  [4, 6, 4]

After the u byte there are the following bytes: 0x03 0x04 0x06 0x04

Python 2, 57 64 bytes

Edit Corrected with the addition of 7 bytes after feedback from @Dada. Thanks!

i,j=input,''
for x in i():j+=`len(x.split())`+' '
i(j=='5 7 5 ')

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Not the shortest Python answer by a long way but just wanted to use the new trick I learned recently of using input() to display the output and save a print statement. Takes a list of lines as input. Requires Ctrl C (or any other key-press for that matter) to terminate the program (with an exception) in a terminal but works fine without on TIO.

MATL, 16 bytes

"@Y:Ybn&h][ACA]=

The input is a cell array of strings and returns a truthy or falsey array.

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Explanation

        % Implicitly grab input
"       % For each element in the cell array
@Y:Yb   % Split it on spaces
n       % Count the number of elements
&h      % Horizontally concatenate everything on the stack
[ACA]   % Create the array [5 7 5]
=       % Perform an element-wise equality
        % Implicitly display the truthy/falsey array

MATLAB / Octave, 38 bytes

@(x)cellfun(@(y)sum(y==32),x)==[4 6 4]

This solution accepts a cell array of strings as input, counts the number of spaces in each line and then compares the result to the array [4 6 4] and yields a truthy (all values are 1) or falsey (any value is zero) array.

Online demo

Perl 6, 25 bytes

{.lines».words~~(5,7,5)}

J, 12 bytes

4 6 4=#@;:@>

The input is a boxed list of strings.

Explanation

This is a fork with a constant left tine. This checks the result of the right tine, #@;:@>, for equality with 4 6 4. The right time unboxes each (>), then (@) converts each string to words (;:), then (@) takes the length of each (#).

Java (OpenJDK), 82 bytes

s->s[0].split(" ").length==5&&s[2].split(" ").length==5&&s[1].split(" ").length==7

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It looks so golfable but without a builtin map function, I can't find a good way. Iterating through the array is a few bytes longer, as is writing a map function using streams.

Lambda expression takes an array of Strings and returns a Boolean.

C++ 357 bytes

Sort of new to code golf, but this is the best I could do quickly

#include <iostream>
using namespace std;
int n(std::string s)
{
    int b = 0;
    for(char c: s)
        if(c == ' ') b++;
    cout << "C = " << b;
    return b;
}
int main()
{
    string a, b, c;
    getline(cin, a);
    getline(cin, b);
    getline(cin, c);
    if(n(a)==4 && n(b)==6 && n(c)==4)
        cout<<'1';
    else cout << '0';
    return 0;
}

R, 48 bytes

all(stringr::str_count(scan(,"")," ")==c(4,6,4))

Reads a 3-length character vector from stdin and works by counting the number of spaces. To count the number of spaces we use the str_count from the stringr package which can count occurrences based on a regex pattern.

An alternative approach without using packages could be:

all(sapply(scan(,""),function(x)length(el(strsplit(x," "))))==c(5,7,5))

Japt, 11 bytes

Saved lots of bytes thanks to @ETHproductions

This takes an array of three strings as input.

®¸lÃ¥"5,7,5

Run it online!

PowerShell, 43 bytes

"$args"-replace'\S'-match'^(    )
\1  
\1$'

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Explanation

Takes input as a newline separated string.

Removes all non-whitespace, then checks to see that it matches "4 spaces, newline, 6 spaces, newline, 4 spaces newline" exactly, using a regex.

The capture group matches 4 spaces, the backreference \1 refers to that. Newlines are embedded in the string. Note the second line of the regex contains two spaces after the backreference.

Clojure, 44 bytes

#(=(for[l %](count(filter #{\ }l)))'(4 6 4))

Input is list of strings. Function finds only spaces and counts them. This explanation is a Haiku. :)

SmileBASIC, 96 bytes

INPUT A$,B$,C$?C(A$,4)*C(B$,6)*C(C$,4)DEF C(S,E)WHILE LEN(S)INC N,POP(S)<"!
WEND
RETURN N==E
END

R, 100 bytes

f<-function(a){all(sapply(a,function(x){length(grep(" ",as.list(strsplit(x,"")[[1]])))})==c(4,6,4))}

Takes as an argument a length-3 list of strings. Probably won't be golfed further since further golfing turns it into @Billywob's answer.

Java 7, 154 bytes

class M{public static void main(String[]a){System.out.print(a.length==3&&a[0].split(" ").length==5&a[1].split(" ").length==7&a[2].split(" ").length==5);}}

The program requirement and potential of having less or more than three lines, not too mention Java's verbosity itself, causes this 'golfed' code to be pretty big..

Ungolfed:

Try it here.

class M{
  public static void main(String[] a){
    System.out.print(a.length == 3
        && a[0].split(" ").length == 5
         & a[1].split(" ").length == 7
         & a[2].split(" ").length == 5);
  }
}