Why can we use mathematical induction to prove that $2^n \ge n^2$ for $ n \ge 5$ Why can we use mathematical induction to prove that $2^n \ge n^2$ for $ n \ge 5$

Normally, the proof via mathematical induction starts with $n =1$. Why does it still hold, when we start with other numbers?
if you insist, you can define $$ n = m+4 $$ and begin with $m=1$
multiplying $$2^k\geq k^2$$ by $2$ we get
$$2^{k+1}\geq 2k^2$$ now you have to prove that $$2k^2\geq (k+1)^2$$