Important property: \((\sqrt[a]{k})^b=k^{\frac{b}{a}}\)

Given: \((\sqrt[3]{25})^x=5\)

Apply property to get: \(25^{\frac{x}{3}}=5\)

Rewrite both sides as follows: \((5^2)^{\frac{x}{3}}=5^1\)

Apply Power of a Power law to left side: \(5^{\frac{2x}{3}}=5^1\)

Since the bases both equal 5, we can conclude that \(\frac{2x}{3}=1\)

Multiply both sides by \(3\) to get: \(2x = 3\)

Divide both sides by \(2\) to get: \(x = \frac{3}{2}\)

Answer: C

Cheers,
Brent