Correct Answer: $7 \frac{1}{4}$

Solution : $2x^2 – 7x + 5 = 0$
$⇒2x^2 + 5 = 7x$
Dividing by $2x$, we get,
$⇒x + \frac{5}{2x} = \frac{7}{2}$
Squaring both sides, we get,
$⇒(x + \frac{5}{2x})^2 = (\frac{7}{2})^2$
$⇒x^2 + (\frac{5}{2x})^2 + 2 × x × \frac{5}{2x} = \frac{49}{4}$
$⇒x^2 + \frac{25}{4x^2} + 5 = \frac{49}{4 }$
$⇒x^2 + \frac{25}{4x^2} = \frac{49}{4} - 5$
$⇒x^2 + \frac{25}{4x^2} = \frac{29}{4}$
$\therefore x^2 + \frac{25}{4x^2} = 7\frac{1}{4}$
Hence, the correct answer is $7\frac{1}{4}$.