$f(g(x))=\frac{1}{\frac{3}{x}+5-5}$

Step 1 ：The given function is $f(g(x))=\frac{1}{\frac{3}{x}+5-5}$.

Step 2 ：First, simplify the denominator of the fraction. The denominator is $\frac{3}{x}+5-5$. The terms $+5$ and $-5$ cancel each other out, leaving us with $\frac{3}{x}$.

Step 3 ：So, the function simplifies to $f(g(x))=\frac{1}{\frac{3}{x}}$.

Step 4 ：Next, simplify the fraction $\frac{1}{\frac{3}{x}}$. This is a complex fraction, and it can be simplified by multiplying the numerator and the denominator by $x$.

Step 5 ：The simplified expression is $\frac{x}{3}$.

Step 6 ：Final Answer: $f(g(x))=\boxed{\frac{x}{3}}$