Let (h, k) lie on the circle C: x^2+y^2=4 and the point (2 h+1,3 k+2) lie on an ellipse with eccentricity e. Then the value of 5/e^2 is equal to ____.

Let $\displaystyle (h, k)$ lie on the circle $\displaystyle \mathrm{C}: x^2+y^2=4$ and the point $\displaystyle (2 h+1,3 k+2)$ lie on an ellipse with eccentricity $\displaystyle e$. Then the value of $\displaystyle \frac{5}{e^2}$ is equal to $\displaystyle \_\_\_\_$.