Answer
$6.4\times10^{-15}m$.
Work Step by Step
The energy levels are given by the equation $E_n=\frac{n^2h ^2}{8mL^2}$.
The ground state has n=1. Solve for L. From the problem statement, $E_1=5.0\times10^6 eV=8.0\times10^{-13}J$.
$$L=\frac{h}{\sqrt{8mE_1}}=6.4\times10^{-15}m $$
This is approximately the size of a nucleus.