Why is $\pi_3(S^2\cup_f e^4)=\mathbb{Z}_5$?

Question

In the space $S^2\cup_f e^4$, $f:=S^3\to S^2$ with Hopf invariant 5. I can't see why $\pi_3(S^2\cup_f e^4)=\mathbb{Z}_5$.

Thanks!