The equation is
${\left[1+{\left(\frac{\mathit{d}\mathit{y}}{\mathit{d}\mathit{x}}\right)}^2\right]}^5={\left(\frac{{\mathit{d}}^2}{\mathit{y}}\mathit{d}{\mathit{x}}^2\right)}^1$
The highest derivative is ${\left(\frac{{\mathit{d}}^2}{\mathit{y}}\mathit{d}{\mathit{x}}^2\right)}^1$
$\Rightarrow$ Order of differential equation is 2
$\Rightarrow$ The exponent of highest derivative is 1
Therefore, degree of differential equation is 1