jmc

We have $i^5=i^4\cdot i=1\cdot (i)=i$. We also have $i^{-25}=1/i^{25}=1/(i^{24}\cdot i)=1/[1\cdot (i)]=1/i=\frac{1}{i}\cdot \frac{i}{i}=i/(-1)=-i$ and $i^{45}=(i^{44})\cdot i=1\cdot i=i$, and . So, adding these three results gives $i^5+i^{-25}+i^{45}=i+-i+i=\boxed{i}$.