1. **State the problem:** Solve the equation $$\frac{5^{3-y}}{\pi} = 2$$ for $y$. 2. **Isolate the exponential term:** Multiply both sides by $\pi$ to get rid of the denominator. $$5^{3-y} = 2\pi$$ 3. **Take the logarithm of both sides:** Use the natural logarithm $\ln$ to solve for the exponent. $$\ln\left(5^{3-y}\right) = \ln(2\pi)$$ 4. **Use the logarithm power rule:** Bring down the exponent. $$ (3 - y) \ln(5) = \ln(2\pi) $$ 5. **Solve for $y$:** $$ 3 - y = \frac{\ln(2\pi)}{\ln(5)} $$ $$ y = 3 - \frac{\ln(2\pi)}{\ln(5)} $$ 6. **Final answer:** $$\boxed{y = 3 - \frac{\ln(2\pi)}{\ln(5)}}$$ This is the exact value of $y$ in terms of natural logarithms.