Answer
The function is not a solution of the differential equation.
Work Step by Step
Begin by solving for the 4th derivative of y.
$y= 5\ln{x}$
$y'= \frac{5}{x}$
$y''=- \frac{5}{x^2}$
$y'''= \frac{10}{x^3}$
$y^{(4)}= -\frac{30}{x^4}$
Substitute back into the differential eqution.
$y^{(4)} -16y=0$
$-\frac{30}{x^4} -80\ln{x} \ne 0$
Since both sides are not equal, the function is not a solution of the differential equation.
