Find and simplify the difference quotient $\frac{f(x+h)-f(x)}{h}, h \neq 0$ for the given function \[ f(x)=5 x^{2} \] \[ \frac{f(x+h)-f(x)}{h}=\square \text { (Simplify your answer.) } \]

Step 1 ：Substitute \(x+h\) into the function to get \(f(x+h) = 5(x+h)^2\).

Step 2 ：Subtract \(f(x)\) from this to get \(f(x+h) - f(x) = 5(x+h)^2 - 5x^2\).

Step 3 ：Divide this by \(h\) to get the difference quotient.

Step 4 ：Simplify the difference quotient to get \(5h + 10x\).

Step 5 ：The simplified difference quotient is \(\boxed{5h + 10x}\).