Reduce the complex fraction $\frac{5 y+\frac{1}{x-5}}{\frac{3 x+1}{3}}$. (A) $\frac{15 x y+75 y+3}{3 x^{2}+14 x-5}$ (B) $\frac{15 x y+75 y}{3 x^{2}-5}$ (C) $\frac{15 x y+3}{3 x^{2}+5}$ (D) $\frac{15 x y-75 y+3}{3 x^{2}-14 x-5}$

Step 1 ：Given the complex fraction $\frac{5 y+\frac{1}{x-5}}{\frac{3 x+1}{3}}$

Step 2 ：To simplify this fraction, we need to find the least common multiple (LCM) of the denominators of the fractions in the numerator and the denominator. In this case, the LCM is $(x-5)*3$

Step 3 ：We then multiply the numerator and the denominator by the LCM. This gives us the fraction $\frac{27*(x - 5)*(5*y*(x - 5) + 1)}{(3*x + 1)}$

Step 4 ：Simplifying this fraction gives us $\frac{15 x y-75 y+3}{3 x^{2}-14 x-5}$

Step 5 ：Comparing this with the options given, we find that it matches with option (D)

Step 6 ：So, the final answer is \(\boxed{(D) \frac{15 x y-75 y+3}{3 x^{2}-14 x-5}}\)