What is X plus 5 equals x minus 5?

Answer 1

x+5=x-5 can be written as
x=x-5-5 so x-x=-10 or 0=-10

we end up with 0=-10 which is not true. This tells us the there is no solution.
One way to see this is think of the line y=x+5, this is a line with slop 1 and y intercept 5.
Now the other line y=x-5 has slope 1 also and y intercept -5.
When we set the two equations equal to one another, we are asking, what is the intersection of the graphs of the two lines. Since they have the same slope and different y intercepts, the lines are parallel and hence have no intersection.