Try this one on your own. All these induction proofs with sums follow the same pattern
Show for a base (usually n=1)
Suppose P(n) which is "5 + 10 + 15 + ... + 5n = 5n(n+1)/2"
Show P(n+1) supposing P(n)
with these sums, it amounts to this for P(n+1)
5 + 10 + 15 + ... + 5n + 5(n+1)
but what is the bolded part equal to according to assumption? can you finish?