Simplify the algebraic expression. \[ 5(5 x+2)-7 \] \[ 5(5 x+2)-7= \]

Step 1 ：Distribute the 5 across the terms inside the parentheses: \(5(5x+2) = 25x + 10\)

Step 2 ：Subtract 7 from the result: \(25x + 10 - 7 = 25x + 3\)

Step 3 ：Final Answer: \(\boxed{25x + 3}\)