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by riquito 4464 days ago
There are 1160290625000000000000000 combinations of 5 words with a dictionary of 65000 words. That's not brute-forceable. If you take existing phrases it's another story, but random words works well.
2 comments

Being a little loose with my estimates and a bit of Fermi Math, thats only about 300 years of computing time on a small home built GPU cluster.

Basically tells me that 4 random words are definitely crackable and 5 are theoretically possible (and definitely doable with 5-10 years of Moore's law)

lg(65k^4) is very nearly 64. If you worry about 4 random words being brute forced, you should worry about 64 bit symmetric keys being brute forced. I don't know where the current recommendations come down on that.
not sure what your calculation is, but permutations is what you should have calculated.
His calculation was (65000 Choose 5) * 5!. His premise required a combination then a permutation.