There are a few small items worth pointing out. As can be seen in the sample below, DATA is special: avoid using it in other roles to avoid confusion.

It is strongly recommended that you use the three parameter version of open. The intent is clearer and where a file name is provided the three parameter open is much safer. It looks like open (INFILE, '<', 'AXP_FACS.DAT'); (many people omit the parentheses).

Using a Perl for loop is generally much preferred over the C style for. Combined with the range operator the intent is much clearer and less prone to off by one errors: for (1 .. 5000) {.

A cleaned up version of the code might look like:

use strict;
use warnings;

my %faclist;

while (<DATA>) {
    chomp;
    $faclist{$_}++;
}

for (1 .. 5000) {
    if (exists $faclist{$_}) {
        print "Found $faclist{$_} of $_\n";
    }
}

__DATA__
1
1090
wibble
1
[download]

Prints:

Found 2 of 1
Found 1 of 1090
[download]

An interesting variation of the print loop that you might like to ponder is:

print "Found $faclist{$_} of $_\n"
    for sort {$a <=> $b} grep {/^\d+$/} keys %faclist;
[download]