$7 \tan x \cos x=5$

Step 1 ：Rewrite the equation in terms of sine and cosine: \(7 \frac{\sin x}{\cos x} \cos x = 5\)

Step 2 ：Simplify the equation: \(7 \sin x = 5\)

Step 3 ：Divide both sides by 7: \(\sin x = \frac{5}{7}\)

Step 4 ：Find the value of x: \(x \approx 0.7956\)

Step 5 ：\(\boxed{x \approx 0.7956}\)