If you just want the intersection of the two arrays and all values are unique within each array, something like this should work:

#!/usr/bin/perl -w

use strict;

my @array1 = qw[a b c d e];
my @array2 = qw[a n o t h e r];

my %count;
foreach my $element (@array1, @array2) {
  $count{$element} += 1;
}
foreach my $key (keys %count) {
  print "$key appears in both arrays\n" if $count{$key} == 2;
}
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Output:

$ ./foo.pl 
a appears in both arrays
e appears in both arrays
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For something a little more complex (but also more robust, more flexible, and probably faster) you could do this:

#!/usr/bin/perl -w

use strict;

my @array1 = qw[a b c d e];
my @array2 = qw[t e s t d a t a];

my @sort1 = sort @array1;
my @sort2 = sort @array2;

while (@sort1 && @sort2) {
  if ($sort1[0] eq $sort2[0]) {
    my $match = $sort1[0];
    while (@sort1 && $sort1[0] eq $match) { shift @sort1; }
    while (@sort2 && $sort2[0] eq $match) { shift @sort2; }
    print "$match is in both arrays\n";
  } elsif ($sort1[0] lt $sort2[0]) {
    shift @sort1;
  } else {
    shift @sort2;
  }
}
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which produces

$ ./bar.pl 
a is in both arrays
d is in both arrays
e is in both arrays
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without getting a false positive on 't' like the first version would.