Determine the derivative of the function: $f(x)=5 x-\cos (5 x)$

Step 1 ：The question is asking for the derivative of the function \(f(x)=5x-\cos(5x)\). To find the derivative of this function, we can use the power rule and the chain rule. The power rule states that the derivative of \(x^n\) is \(nx^{n-1}\). The chain rule states that the derivative of a composite function is the derivative of the outer function times the derivative of the inner function. In this case, the outer function is \(-\cos(x)\) and the inner function is \(5x\).

Step 2 ：Using the power rule, the derivative of \(5x\) is \(5\).

Step 3 ：Using the chain rule, the derivative of \(-\cos(5x)\) is \(5\sin(5x)\).

Step 4 ：Adding these two derivatives together, we get the derivative of the function \(f(x)=5x-\cos(5x)\) is \(5+5\sin(5x)\).

Step 5 ：Final Answer: The derivative of the function \(f(x)=5x-\cos(5x)\) is \(\boxed{5+5\sin(5x)}\).