Start by adding √(x - 3) to both sides (whatever operation you do to one side of an equation you must do to the other side as well). The result is this:

√(x + 5) = √(x - 3) + 2

Then square both sides to get this:

x + 5 = x - 3 + 2√(x - 3) + 2√(x - 3) + 4

Combine like terms:

x + 5 = x + 1 + 4√(x - 3)

Subtract x and 1 from both sides:

4 = 4√(x - 3)

Divide by 4 to get this result:

1 = √(x - 3)

Square both sides again to get this result:

1 = x - 3

x = 4

Check this solution with the original equation. It always helps to check your work!

I hope this helps.