Correct Answer: $3\frac{3}{5}$

Solution : Given: $5x+\frac{1}{x}=10$
We know that the algebraic identity, $(a+b)^2=a^2+b^2+2ab$.
$5x+\frac{1}{x}=10$
On squaring both sides of the above equation, we get,
$(5x+\frac{1}{x})^2=10^2$
⇒ $25x^2+\frac{1}{x^2}+10=100$
⇒ $25x^2+\frac{1}{x^2}=90$
Divide by 25 on both sides of the above equation, we get,
$x^2+\frac{1}{25x^2}=\frac{90}{25}$
⇒ $x^2+\frac{1}{25x^2}=\frac{18}{5}=3\frac{3}{5}$
Hence, the correct answer is $3\frac{3}{5}$.