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.
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