If $\sqrt{15}=3.8729$, then the value of $\frac{\sqrt{5}+\sqrt{3}}{\sqrt{5}-\sqrt{3}}$ is:

To evaluate the expression, let us rationalize the denominator by multiplying both the numerator and the denominator by $(\sqrt{5}+\sqrt{3})$:
$$\frac{\sqrt{5}+\sqrt{3}}{\sqrt{5}-\sqrt{3}}\times \frac{\sqrt{5}+\sqrt{3}}{\sqrt{5}+\sqrt{3}}=\frac{(\sqrt{5}+\sqrt{3}{)}^2}{(\sqrt{5}{)}^2-(\sqrt{3}{)}^2}$$

Using the algebraic identities $(a+b{)}^2=a^2+b^2+2ab$ and $(a-b)(a+b)=a^2-b^2$:

$$\text{Expression}=\frac{5+3+2\sqrt{15}}{5-3}$$

$$\text{Expression}=\frac{8+2\sqrt{15}}{2}$$

$$\text{Expression}=4+\sqrt{15}$$

Given that $\sqrt{15}=3.8729$:

$$\text{Value}=4+3.8729=7.8729$$