$\sqrt{2 w+13}=\sqrt{5 w+7}$

Step 1 ：Square both sides of the equation to get rid of the square root: \((2w + 13) = (5w + 7)\).

Step 2 ：Rearrange the equation to isolate w: \(w = 2\).

Step 3 ：Substitute the solution back into the original equation to check if it is valid: \(\sqrt{2*2+13} = \sqrt{5*2+7}\).

Step 4 ：The solution w = 2 is valid as it satisfies the original equation.

Step 5 ：Final Answer: \(\boxed{2}\)