If $\log _{2}(5 x+3)=4$, then $x=$

Step 1 ：Convert the logarithmic equation \(\log _{2}(5 x+3)=4\) into an exponential equation. The base of the logarithm becomes the base of the exponent, the right side of the equation becomes the exponent, and the argument of the logarithm becomes the result. So, the equation becomes \(2^4 = 5x + 3\).

Step 2 ：Simplify the equation to get \(16 = 5x + 3\).

Step 3 ：Subtract 3 from both sides of the equation to isolate the term with x. The equation becomes \(13 = 5x\).

Step 4 ：Divide both sides of the equation by 5 to solve for x. The solution to the equation is \(x = \frac{13}{5}\).

Step 5 ：Substitute \(x = \frac{13}{5}\) into the original equation to verify the solution. The equation holds true.

Step 6 ：Final Answer: \(x = \boxed{\frac{13}{5}}\)