At first glance I believe you meant 10 = (3/5)(x+5). It's important that you share the instructions for each problem you post; I assume they state: "solve the following fractional linear equation for x."
Here are two approaches. Take your pick.
1) Distribute the multiplier (3/5) over (x+5). Resulting equation is
10=(3/5)x + 3. Subtr. 3 from both sides: 7=(3/5)x. Mult both sides by (5/3). Result: (35/3)=x.
2) Mult. the original equation by 5 to remove fractions: 50=3(x+5). Multiply out 3(x+5), to obtain 50=3x +15. Subtr. 15 from both sides. Result:
35=3x. Divide both sides by 3.