The process is to go step-by-step to isolate the y.
To do this, you basically run the order of operations in reverse.
In 5x+2y=10, the first thing to move away from the left side is 5x and you cancel it out by subtracting 5x from both sides:
5x+2y - 5x = 10 - 5x
The 5x's on the left cancel leaving you with:
2y = 10 - 5x
Side note: this is more commonly written as 2y = -5x+10, since we tend to write variable terms first.
Finally, to get the y fully by itself, you need to cancel the 2 that's multplied against it. To cancel multiplication, you need to divide:
[tex]\dfrac{2y}{2} = \dfrac{-5x+10}{2}[/tex]
The most important thing to remember here is that the 2 needs to divide into both terms on the right:
[tex]\dfrac{2y}{2} = \dfrac{-5x}{2}+ \dfrac{10}{2}[/tex]
Finally, we simplify this into:
[tex]y = -\dfrac{5}{2}x+5[/tex]
