Solve and check. (If there is no solution,
\[
\sqrt{5 x}-8=-6
\]

Step 1 ：The given equation is \(\sqrt{5x} - 8 = -6\).

Step 2 ：To solve for \(x\), we first need to isolate the square root term. We can do this by adding 8 to both sides of the equation. This will give us \(\sqrt{5x} = 2\).

Step 3 ：Then, we can square both sides of the equation to get rid of the square root, which will give us \(5x = 4\).

Step 4 ：Finally, we can solve for \(x\) by dividing both sides of the equation by 5. This gives us \(x = 0.8\).

Step 5 ：We can confirm this is correct because when we substitute \(x = 0.8\) back into the original equation, we get 0, which means the left and right sides of the equation are equal.

Step 6 ：The solution to the equation \(\sqrt{5x} - 8 = -6\) is \(\boxed{0.8}\).