The handling of $_ is somewhat magical, and provided by the perl parser - not by the angle brackets. When perl sees this:

while (<>) {
}
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It actually does this:

while (defined($_ = <ARGV>)) {
    ();
}
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You can verify this yourself using B::Deparse. Here is an example (assume test.pl as filename):

  perl -MO=Deparse test.pl
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Problems:

1. By adding the test for $i <= 4 to the while loop you caused perl to skip the magical behaviour for while(<>).
2. You should chomp the data that is being read in, otherwise instead of "1" you will have "1\n"

Suggestions:

1. It is a better practice to use push instead of (@arr1,$_)
2. use warnings instead of perl -w

New version of the code that addresses the above

#!/usr/bin/perl
use strict;
use warnings;
print "Enter 5 numbers: \n";

my $i=0;
my @arr1=();

while (<>) {
    chomp;
    push @arr1, $_;
    last if ++$i > 4;
}

foreach my $m (@arr1) {
   print $m, "\n";
}
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Update

Additionally, please read How To Ask A Question - Choose a Good, Descriptive Title