Mituna was doing his calculus homework. He came across this integral, but he got stuck, so he asked Latula for help. Latula, who is the master of all things radical, showed him this. $\int_0^{16}\sqrt{5+\sqrt{x}}\text{ }dx=\dfrac{A+B\sqrt{C}}{D}$ What is $A+B+C+D?$