#### Answer

$x=14.7$

#### Work Step by Step

Let us start with the given equation: $\frac{2x}{7}+\frac{4}{5}=5$
We multiply by $35$, the least common denominator, to clear the fractions: $35(\frac{2x}{7}+\frac{4}{5}=5)$
We use the distributive property to multiply $35$ by each of the inner terms: $10x+28=175$
Next, we subtract $28$ from both sides: $10x+28-28=175-28$
We combine the like terms: $10x=147$
Finally, we divide by $10$ on both sides of the equation: $x=\frac{147}{10}=14.7$