Solve.
\[
\sqrt[5]{5 x-5}=\sqrt[5]{6 x+8}
\]

Step 1 ：Given the equation \(\sqrt[5]{5x-5}=\sqrt[5]{6x+8}\)

Step 2 ：Raise both sides of the equation to the power of 5 to remove the fifth root. This gives us the equation \((5x - 5)^5 = (6x + 8)^5\)

Step 3 ：Solving this equation gives us five potential solutions: \[-13, -\frac{3501}{9302} - \frac{385\sqrt{5}}{9302} - \sqrt{-\frac{56233625}{43263602} - \frac{22418725\sqrt{5}}{43263602}}, -\frac{3501}{9302} - \frac{385\sqrt{5}}{9302} + \sqrt{-\frac{56233625}{43263602} - \frac{22418725\sqrt{5}}{43263602}}, -\frac{3501}{9302} + \frac{385\sqrt{5}}{9302} - \sqrt{-\frac{56233625}{43263602} + \frac{22418725\sqrt{5}}{43263602}}, -\frac{3501}{9302} + \frac{385\sqrt{5}}{9302} + \sqrt{-\frac{56233625}{43263602} + \frac{22418725\sqrt{5}}{43263602}}\]

Step 4 ：However, the original equation only makes sense for real numbers, because we can't take the fifth root of a negative number. Therefore, we need to check which of these solutions are real.

Step 5 ：The only real solution is -13.

Step 6 ：So, the final solution to the equation is \(\boxed{-13}\)