Let $$y:(-\infty,\infty)\to(0,\infty)$$ be the solution of the differential equation

$$\dfrac{dy}{dx}=\dfrac{e^{5x}y^3+y^3}{e^x+e^x y^4},$$

satisfying $$y(0)=\dfrac{1}{\sqrt{2}}$$. Then the value of $$y(\log_e 2)$$ is

A

$$\sqrt{\dfrac{5+\sqrt{35}}{2}}$$

B

$$\sqrt{\dfrac{7+\sqrt{53}}{2}}$$

C

$$\dfrac{7+\sqrt{53}}{2}$$

D

$$\dfrac{5+\sqrt{35}}{2}$$