jmc

Since $-7<-5$, $f(-7)=3$. Since $-5\le 0\le 5$, $f(0)=2(0)-3=-3$. Since $7>5$, $f(7)=7^2+1=50$. Therefore, $f(-7)+f(0)+f(-7)=3-3+50=\boxed{50}$.