This shoudl be a little quicker. It uses a bit vector rather than a hash which is a bit quicker to start. It then scans the bit vector 64-bits at a time until it finds a possibility and then by bit until it isolates the next value:

#! perl -slw
use strict;

my @ports = ( 50000..51545,51549,51555..51999, 65535 );

my $vec = '';
vec( $vec, $_, 1 ) = 1 for 0 .. 50_000, @ports;

sub nextFreePort {
    no warnings 'portable';
    my $open_port;
    my $t = int( length( $vec ) / 8 );
    my $n = 782;
    ++$n while $n <= $t and vec( $vec, $n, 64 ) == 1844674407370955161
+5;
    $n *= 64;
    vec( $vec, $_, 1 ) or $open_port = $_ and last for $n .. $n + 64;
    vec( $vec, $open_port, 1 ) = 1;
    return $open_port;
}

my $next_port = nextFreePort();
print $next_port;

__END__
c:\test>899314.pl
51546
[download]

Worst case of only 65535 being available, it does 242+63 tests+incs, rather than 15500.

If I were writing this in assembler, I'd test lo/hi 32-bit; lo/hi 16-bit; lo/hi 8-bit before hitting the bits individually thereby reducing the 63 tests/incs to 10.

It require 8k of string which is quite possibly smaller than your hash. That coudl be reduced further by not storing bits for 0 .. 50_000.

It's a POC. I haven't tested the edge cases.