All the questions are almost same try them after seeing this

P(n) :2^n - n^2 >0 When n>4

First step:

Now 7 >0 hence its correct for n = 5

Assumption :P(k) is correct

ie;

Hence

Proof for P(k+1) using assumption:

since

Hence

But since (k+1)^2 is always a positive number (greater than 16 atleast ) thus proved that its correct for k+1 hence through the principle of mathematical induction this is proved