Solve the exponential equation by expressing each side as a power of the same base and then equating exponents. \[ 8^{x}=32 \]

Step 1 ：Rewrite the equation \(8^{x}=32\) as \((2^3)^x = 2^5\)

Step 2 ：Simplify to get \(2^{3x} = 2^5\)

Step 3 ：Since the bases are the same, equate the exponents to get \(3x = 5\)

Step 4 ：Solve for x to get \(x = \frac{5}{3}\)

Step 5 ：Final Answer: The solution to the equation \(8^{x}=32\) is \(x=\boxed{\frac{5}{3}}\)