Correct Answer: $\frac{19}{4}$

Solution : Given;
$2x-\frac{1}{2x}=5,x\neq0$
Dividing both sides by 2, we get
$x-\frac{1}{4x}=\frac{5}{2}$
Now, squaring both sides, we get
$(x^2+\frac{1}{16x^2}-2×x×\frac{1}{4x})=\frac{25}{4}$
⇒$(x^2+\frac{1}{16x^2})=\frac{25}{4}+\frac{1}{2}$
⇒$(x^2+\frac{1}{16x^2})=\frac{27}{4}$
⇒$(x^2+\frac{1}{16x^2}-2)=\frac{27}{4}-2$
$\therefore (x^2+\frac{1}{16x^2}-2)=\frac{19}{4}$
Hence, the correct answer is $\frac{19}{4}$.