Find and simplify the difference quotient $\frac{f(x+h)-f(x)}{h}, h \neq 0$ for the given function.
\[
f(x)=-5 x
\]

Step 1 ：We are given the function \(f(x) = -5x\).

Step 2 ：We need to find and simplify the difference quotient \(\frac{f(x+h)-f(x)}{h}\), where \(h \neq 0\).

Step 3 ：Substitute \(f(x+h)\) and \(f(x)\) into the difference quotient formula: \(f(x+h) = -5(x+h)\) and \(f(x) = -5x\).

Step 4 ：Subtract \(f(x)\) from \(f(x+h)\) to get \(-5h\).

Step 5 ：Divide \(-5h\) by \(h\) to get \(-5\).

Step 6 ：So, the simplified difference quotient for the function \(f(x) = -5x\) is \(\boxed{-5}\).

Step 7 ：This means that the average rate of change of the function over the interval h is -5. This is consistent with the fact that the function is a linear function with a slope of -5.