If tanθ + secθ = 7, θ being acute, then the value of 5sinθ is:

Answer: Option D

$$\begin{array}{rl}& \sec \theta +\tan \theta =\mathrm{7........}\left(\text{i}\right)\\ & \sec \theta -\tan \theta =\frac{1}{7}........\left(\text{ii}\right)\\ & \text{From equation }\left(\text{i}\right)\text{ and }\left(\text{ii}\right)\\ & 2\sec \theta =7+\frac{1}{7}=\frac{50}{7}\\ & \sec \theta =\frac{25\to h}{7\to b}p=24\\ & \sin \theta =\frac{24}{25}\\ & 5\sin \theta =5\times \frac{24}{25}=\frac{24}{5}\end{array}$$