2. By Fermats little $\displaystyle 5^{12} \equiv 1 \pmod {13}$ so $\displaystyle 5^{99}=5^{12 \cdot 8}\cdot 5^{3} \equiv 5^3 \pmod{13}$
It's left to find the rest for $\displaystyle 5^3$ when it's divided by 13 and I leave this to you.