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

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