Welcome to the forum.

First, we usually say "equal" referring to numbers and "equivalent" referring to propositions. This is because "equal" usually means "identical." In contrast, two propositions are equivalent if they imply each other, and they an be very different otherwise. There are even examples of equivalent propositions P and Q such that P is intuitively true and Q is intuitively false for many people (of course, their intuition is incorrect in this case).

As you said, you have for any n >= 5. Since k >= 5 (this has to be stated as an assumption), instantiate n with k to get . Since , we have , which concludes the inductive step.

Don't forget the base case, when >= turns into =.