Q2: Sum of the order and degree of $\frac{d}{dx}\left(\frac{dy}{dx}\right) = 5$

$\frac{d}{dx}\left(\frac{dy}{dx}\right)$ means: differentiate $\frac{dy}{dx}$ once more. That is the second derivative, written $\frac{d^2y}{dx^2}$⁠.

Always rewrite the equation in this simple form before reading off the order and the degree.

The order of a differential equation is the order of the highest derivative in it. A second derivative gives order 2.

The degree is defined only when the equation is a polynomial in the derivatives: no derivative under a root, in a denominator, or inside a function such as sin. The degree is then the highest power of the highest order derivative.

Here $\frac{d^2y}{dx^2}$ appears to the power 1.

Watch out: the 2 in $\frac{d^2y}{dx^2}$ shows the order, not a power.