Which number completes the analogy 6 : 720 :: 5 : ?

Every whole number from 1 up to the given number is multiplied together. For 6 that is $1\times 2\times 3\times 4\times 5\times 6=720$, so for 5 it is $1\times 2\times 3\times 4\times 5=120$. The trap 125 reads the rule as cubing, but 6 cubed is 216 and not 720. 30 stops after multiplying 5 by 6, and 600 is $5\times 120$, one factor too many.