Induction · Hard problem

"Claim": $n^2 \ge 5n - 5$ for every positive integer $n$. The base $n = 1$ holds ($1 \ge 0$), and the step $(k + 1)^2 = k^2 + 2k + 1 \ge 5k - 5 + 2k + 1 \ge 5(k + 1) - 5$ needs $7k - 4 \ge 5k$, i.e. $k \ge 2$. For how many positive integers $n$ is the claim actually false?