If $a+\dfrac{1}{a}=5$ for a nonzero real number $a$, then the value of $a^2+\dfrac{1}{a^2}$ is

Use the identity $\left(a+\frac{1}{a}\right)^2=a^2+\frac{1}{a^2}+2$. Substituting gives $25=a^2+\frac{1}{a^2}+2$. Hence $a^2+\frac{1}{a^2}=23$.