(5) The correct answer is $(E)$.

Since the expression is the sum of two squares, it vanishes if and only if both quantities are zero. It follows that $y=\frac{3}{4}$ and $6 x-\frac{15}{4}=0$, i.e., $x=\frac{5}{8}$. Therefore, $x+y=\frac{3}{4}+\frac{5}{8}=\frac{11}{8}$. Question proposed by Paolo Francini.
5. The real numbers $x$ and $y$ satisfy the equation $(6 x-5 y)^{4}+(4 y-3)^{6}=0$. What is the value of $x+y$?
(A) 1
(B) $10 / 7$
(C) $4 / 3$
(D) $13 / 9$
(E) $11 / 8$