hi
this can be done easily by factoring the expression you got there:
n(n^2-1)(n^2-4)=n(n-1)(n+1)(n-2)(n+2)=(n-2)(n-1)n(n+1)(n+2)
and this is a product of five consecutive numbers so it is definitely divisible by 5,4,3,2 and 1. note that this is true only if the product above is positive or equal to zero,so it is true only for n>=3 which what you wanted to prove.