Solve for x (5x-7)^(1/3)+3=5

${(5 x - 7)}^{\frac{1}{3}} + 3 = 5$

Move all terms not containing $x$ to the right side of the equation.

Subtract $3$ from both sides of the equation.

${(5 x - 7)}^{\frac{1}{3}} = 5 - 3$

Subtract $3$ from $5$ .

${(5 x - 7)}^{\frac{1}{3}} = 2$

Raise each side of the equation to the power of $3$ to eliminate the fractional exponent on the left side.

${({(5 x - 7)}^{\frac{1}{3}})}^{3} = 2^{3}$

Simplify the exponent.

Simplify the left side.

Simplify ${({(5 x - 7)}^{\frac{1}{3}})}^{3}$ .

Multiply the exponents in ${({(5 x - 7)}^{\frac{1}{3}})}^{3}$ .

Apply the power rule and multiply exponents, ${(a^{m})}^{n} = a^{m n}$ .

${(5 x - 7)}^{\frac{1}{3} \cdot 3} = 2^{3}$

Cancel the common factor of $3$ .

Cancel the common factor.

${(5 x - 7)}^{\frac{1}{3} \cdot 3} = 2^{3}$

Rewrite the expression.

${(5 x - 7)}^{1} = 2^{3}$

Simplify.

$5 x - 7 = 2^{3}$

Simplify the right side.

Raise $2$ to the power of $3$ .

$5 x - 7 = 8$

Solve for $x$ .

Move all terms not containing $x$ to the right side of the equation.

Add $7$ to both sides of the equation.

$5 x = 8 + 7$

Add $8$ and $7$ .

$5 x = 15$

Divide each term in $5 x = 15$ by $5$ and simplify.

Divide each term in $5 x = 15$ by $5$ .

$\frac{5 x}{5} = \frac{15}{5}$

Simplify the left side.

Cancel the common factor of $5$ .

Cancel the common factor.

$\frac{5 x}{5} = \frac{15}{5}$

Divide $x$ by $1$ .

$x = \frac{15}{5}$

Simplify the right side.

Divide $15$ by $5$ .

$x = 3$