Correct Answer: $\frac{24}{5}$

Solution : Given: $\tan\theta+\sec\theta=7$ --------------------(1)
We know that $\sec^2\theta-\tan^2\theta=1$
⇒ $(\sec\theta+\tan\theta)(\sec\theta-\tan\theta)=1$
⇒ $7×(\sec\theta-\tan\theta)=1$
⇒ $\sec\theta-\tan\theta=\frac{1}{7}$ --------------------(2)
Adding equations (1) and (2) we get,
$2\sec\theta=7+\frac{1}{7}$
⇒ $\sec\theta=\frac{25}{7}$
⇒ $\cos\theta=\frac{7}{25}$
⇒ $\sin\theta=\sqrt{1-(\frac{7}{25})^2}$
⇒ $\sin\theta=\frac{24}{25}$
⇒ $5\sin\theta=\frac{24}{5}$
Hence, the correct answer is $\frac{24}{5}$.