Looking at the problem differently, since you know how big each array is, you can use a hash and one array. In the hash, you store the offset to the beginning of the desired (conceptual) row in the array.

use strict;
use warnings;

my %hash;
my @array;
my $row_length = 5;
my $next_available = 0;

for (qw(cow pig donkey)) {
    $hash{$_} = $next_available;
    for my $col (0..($row_length - 1)) {
        $array[$next_available + $col] = "$_ $col";
    }
    $next_available += $row_length;
}

# What would have been $hash{pig}[3]:
print $array[$hash{pig}+3];
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You could even make a class implementing hashes of fixed-size arrays and give it an indexing method. I'm not going to. :-)