Step 1: Plan the calculation.
Total energy equals the number of uranium nuclei multiplied by the energy released per fission. So we first count the nuclei, then multiply.
Step 2: Find the number of moles.
With $5$ g of $^{235}$U, the moles are $n = \frac{5}{235}$.
Step 3: Convert moles to number of nuclei.
\[ N = \frac{5}{235}\times 6.02\times 10^{23} \approx 1.28\times 10^{22} \]
Step 4: Use the energy per fission.
Each $^{235}$U fission gives about $200$ MeV.
Step 5: Multiply to get total energy in MeV.
\[ E = (1.28\times 10^{22})\times 200\ \text{MeV} \approx 2.56\times 10^{24}\ \text{MeV} \]
Step 6: Convert MeV to joules.
Since $1$ MeV $= 1.6\times 10^{-13}$ J, \[ E \approx 2.56\times 10^{24}\times 1.6\times 10^{-13} \approx 4\times 10^{11}\ \text{J} = 0.4\times 10^{12}\ \text{J} \]
\[ \boxed{E = 0.4\times 10^{12}\ \text{joules}} \]