If E(X^r) =5^r, r = 1, 2, 3, ..., find the moment-generating function M(t) of X and the p.m.f. of X.

The m.g.f. of X is sum((e^tx)*f(x)) of all x in S.

so the mgf of X^r is sum((e^t(X^r))*f(x^r)... this is where I'm lost. Can I get some guidance how to apply the E(X^r) = 5^r to this? Also, do I have to find the pmf first or the mgf? or can I find both from the original statement?

Thank you in advance. (-goes to look up how to use math tags and equations-)