sub is_fibonnacci {
    my $plus = (5 * $_[0] * $_[0]) + 4;
    my $mins = (5 * $_[0] * $_[0]) - 4;
    return is_perfect_square($plus) | is_perfect_square($mins);
}
[download]

No need to calculate 5 * $_[0] * $_[0] twice, and you probably meant to use the logical or operator instead of the bit-wise or operator.

sub is_fibonnacci {
    my $plus = (5 * $_[0] * $_[0]) + 4;
    my $mins = $plus - 8;
    return is_perfect_square($plus) || is_perfect_square($mins);
}
[download]

(The logical operators short-circuit so is_perfect_square($mins) will only execute if is_perfect_square($plus) is true.)

sub is_perfect_square {
    my $sqrt = int(sqrt($_[0]));
    return $sqrt * $sqrt == $_[0];
}
[download]

Or just:

sub is_perfect_square { int( $_[0] ** .5 ) ** 2 == $_[0] }
[download]