jmc

The surface area of a sphere with radius $r$ is $4\pi r^2$. Thus, Theo's sphere has surface area $4\pi (5^2)=100\pi$ and each of Akshaj's spheres have surface area $4\pi (2^2)=16\pi$, so Akshaj's spheres together have surface area $16\pi \cdot 2=32\pi$. The desired ratio is hence $\frac{100\pi }{32\pi }=\boxed{\frac{25}{8}}$.