Binomial coefficients sum problem

Question

I am trying to answer the following problem but I barely understand the question and I've no idea how to proceed.

Calculate the value of $\sum\limits_{k = 0}^n 5^k\binom nk$ for cases where $n = 1,\;2,\;3$.

Could somebody please give me some pointers?

Thanks in advance

Answer 1

By the Binomial Theorem, we have $$\sum_{k=0}^n5^k\binom nk=\sum_{k=0}^n5^k1^{n-k}\binom nk=(5+1)^n=6^n.$$ So, plugging $n=1,2,3$, we get $\boxed{6,36,216}$.