Working with permutations can allegedly be done with Algorithm::Permute, but the number of permutations of 5 out of 3000 is gigantically huge. Using ballpark figures, even if you could test 1 million permutations per second, it would still take you over 7000 years to run through them all. And at the end if it turns out you needed 6 paths instead of 5, you've just wasted the last aeon. Bummer.

So, don't do it that way. :) ELISHEVA's answer is a much better idea.