Let's solve the equation [tex]\(\sqrt[3]{2x + 5} = 5\)[/tex] step-by-step:
1. Eliminate the cube root: To remove the cube root, we need to cube both sides of the equation:
[tex]\[
\left(\sqrt[3]{2x + 5}\right)^3 = 5^3
\][/tex]
[tex]\[
2x + 5 = 125
\][/tex]
2. Isolate the term with [tex]\(x\)[/tex]: Subtract 5 from both sides to isolate the term with [tex]\(x\)[/tex]:
[tex]\[
2x + 5 - 5 = 125 - 5
\][/tex]
[tex]\[
2x = 120
\][/tex]
3. Solve for [tex]\(x\)[/tex]: Divide both sides by 2 to solve for [tex]\(x\)[/tex]:
[tex]\[
\frac{2x}{2} = \frac{120}{2}
\][/tex]
[tex]\[
x = 60
\][/tex]
Therefore, the correct answer is [tex]\(x = 60\)[/tex], which corresponds to option C.
So, the solution to the equation [tex]\(\sqrt[3]{2x + 5} = 5\)[/tex] is:
[tex]\[
\boxed{60}
\][/tex]
