The answer is x = 10
When you cross-multiply, you multiply the numerator on one side by the denominator on the other side. In this case, then, you would have x + 2 multiplied by 5, so 5(x + 2) (In math, when a number is next to a grouping in a parenthesis, that number is multiplying everything in the parenthesis). Then you do the same for x + 5. 4 is multiplied by x + 5, which equals to 4(x + 5). So you have 5(x + 2) = 4(x + 5). This is a case of the distributive property, when the number outside is multiplied by both sides. In the case of 5(x + 2), 5 is multiplied by both x and 2. In the end, you get 5x + 10. If you do the same on 4(x + 5) (multiply 4 on both x and 5), you get 4x + 20. Then you get 5x + 10 = 4x + 20.
Now that these sides are simplified, you choose one of the operations and do its opposite on both sides to isolate x. There are many ways you could do this, but I would subtract 10 on both sides. In 5x + 10, by subtracting 10 you cancel + 10, so you are just left with 5x. On the side of 4x + 20, you subtract 10 from + 20 (you can't subtract 10 from 4x because they are not like terms) which gives you 10. So you have 4x + 10. The equations ends up in 5x = 4x + 10.
Since we want to isolate x, we want to keep x on one side and the rest of the numbers on the other side to find x. In this case, the best option is to subtract 4x from both sides. 5x - 4x equals 1x. In math, when 1 is next to a variable (x), it is just that variable by itself. So 1x = x.
Now that you have x isolated, you have the answer of x = 10.