You already got some great solutions. Here's my 2 cents:

#!/usr/bin/env perl

use strict;
use warnings;
use diagnostics;

use Array::Contains;

my @array1 = ("A2","A5","C1","G0","T3","T4");
my @array2 = ("A2","A3","A5","G1","G0","G4");

foreach my $elem (@array1) {
    print "$elem\n" if(contains($elem, \@array2));
}
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Edit: I just love those kind of Perl questions where there are so many different solutions to choose from. Really shows of the flexibility of the language!