Solve the equation. \[ (x-3)^{2 / 5}=4 \]

Step 1 ：Given the equation \((x-3)^{2 / 5}=4\)

Step 2 ：First, we remove the exponent by taking both sides to the power of its reciprocal, which is \(5/2\). This gives us \((x-3) = 4^{5/2}\)

Step 3 ：Next, we isolate x by adding 3 to both sides. This gives us \(x = 4^{5/2} + 3\)

Step 4 ：Calculating the right side of the equation gives us \(x = 35\)

Step 5 ：Final Answer: The solution to the equation is \(\boxed{35}\)