5. Given that $\operatorname{tg} \theta, \operatorname{ctg} \theta$ are the real roots of the equation $2 x^{2}-2 k x=3-k^{2}$, and $a<\theta<\frac{5 \pi}{4}$, then the value of $\cos \theta-\sin \theta$ is $\qquad$ .
$-\sqrt{\frac{5-2 \sqrt{5}}{5}} ;$