5. The line $y=k x+2$ intersects the right branch of the hyperbola $x^{2}-y^{2}=6$ at two distinct points, then the range of the real number $k$ is
A. $\left(-\frac{\sqrt{15}}{3}, \frac{\sqrt{15}}{3}\right)$
B. $\left(0, \frac{\sqrt{15}}{3}\right)$
C. $\left(-\frac{\sqrt{15}}{3}, 0\right)$
D. $\left(-\frac{\sqrt{15}}{3},-1\right)$
5. $\mathrm{D}$ Hint: The slope of the line tangent to the right branch of the hyperbola is $-\frac{\sqrt{15}}{3}$, and the slope of the line parallel to the asymptote is -1.