A research reactor holds 25 g of uranium-235…

Step 1. The nuclei. $N = \dfrac{25\ \text{g}}{235\ \text{g/mol}} \times 6.022 \times 10^{23}\ \text{mol}^{-1} = 6.41 \times 10^{22}$.

Step 2. The energy. One fission gives $200\ \text{MeV} \times 1.602 \times 10^{-13}\ \text{J/MeV} = 3.20 \times 10^{-11}$ J. So $E = 6.41 \times 10^{22} \times 3.20 \times 10^{-11}\ \text{J} = 2.05 \times 10^{12}$ J.

Step 3. The time. $t = \dfrac{E}{P} = \dfrac{2.05 \times 10^{12}\ \text{J}}{5.0 \times 10^{6}\ \text{W}} = 4.1 \times 10^{5}\ \text{s}$. In days, $\dfrac{4.1 \times 10^{5}}{86\,400} = 4.75$ days.