i'm having trouble understanding strong induction proofs

i understand how to do ordinary induction proofs and i understand that strong induction proofs are the same as ordinary with the exception that you have to assume that the theorem holds forall numbers up to and including some n(starting at the base case) then we try and show: theorem holds for n+1

but how do you show this exactly.

here is a proof by induction:

Thm: n≥1, 1+6+11+16+...+(5n-4) = [n(5n-3)]/2 Proof (by induction)

Basis step: for n=1: 5-4=(5-3)/2 ---> 1=1 the basis step holds

Induction Step: Suppose that for some integer k≥1 1+6+11+16+...+(5k-4) = [k(5k-3)]/2 (inductive hypothesis)

Want to Show: 1+6+11+16+...+(5k-4)+(5{k+1}-4) = [{k+1}(5{k+1}-3)]/2

[k(5k-3)]/2 + (5{k+1}-4) = [{k+1}(5{k+1}-3)]/2

then you just show that they are equal

so how can i do the same proof using strong induction? what are the things i need to add/change in order for this proof to be a strong induction proof?