choice D.
Step-by-step explanation:
Trigonometric Functions
We need to recall some properties and definitions of the trigonometric functions.
![\displaystyle \tan \theta=\frac{\sin\theta}{\cos\theta}](/tpl/images/1060/3750/99162.png)
![\displaystyle \sec \theta=\frac{1}{\cos\theta}](/tpl/images/1060/3750/ae1c8.png)
We need to simplify the following expression:
![5\sin\theta\sec\theta](/tpl/images/1060/3750/5c331.png)
Substituting the identity for the secant:
![\displaystyle 5\sin\theta\sec\theta=5\sin\theta.\frac{1}{\cos\theta}](/tpl/images/1060/3750/aeae9.png)
Operating:
![\displaystyle 5\sin\theta\sec\theta=5\frac{\sin\theta}{\cos\theta}](/tpl/images/1060/3750/e4f02.png)
Substituting the definition of the tangent:
![\displaystyle 5\sin\theta\sec\theta=5\tan\theta](/tpl/images/1060/3750/517e1.png)
Correct choice D.