This was a lot of fun. Basically I expanded each factorial into their prime factorization, and determined that either m or n would need to be larger than 6 so as to include 7 in the factorization. Then just tried to find the other correct matching pair.
mornwould need to be larger than 6 so as to include 7 in the factorization. Then just tried to find the other correct matching pair.10,1was an obvious solution.10,0was not obvious at first but now is :)