According to other monks' messages, below, you can sort short lists in microseconds or nanoseconds. So even though your lists have thousands of elements, I doubt that sorting is the cause of your speed concerns.

Profile your program.

I bet you'll find huge whacks of time spent copying arrays in a function call in an inner loop, where you should be passing a reference, or some other efficiency error. Or it might be your algorithmn that needs some re-thinking. Are you processing things in an item-by-item loop, when you could leave Perl to process the whole set at once?