Simplify the expression by using a double-angle formula. \[ 2 \sin 5 \theta \cos 5 \theta \]

Step 1 ：Given the expression \(2 \sin 5 \theta \cos 5 \theta\).

Step 2 ：This expression is in the form of \(2\sin(a)\cos(a)\), which is a double angle formula in trigonometry.

Step 3 ：The double angle formula for sine is \(\sin(2a) = 2\sin(a)\cos(a)\).

Step 4 ：So, we can simplify the given expression by using this formula.

Step 5 ：Let \(a = 5\theta\), then the expression becomes \(2\sin(a)\cos(a)\).

Step 6 ：Using the double angle formula, this simplifies to \(\sin(2a)\).

Step 7 ：Substituting \(a = 5\theta\) back in, we get \(\sin(10\theta)\).

Step 8 ：Final Answer: The simplified expression using the double-angle formula is \(\boxed{\sin 10 \theta}\).