If I give my brother $5$ dollars, then we will have the same amount of money. If instead he gives me $10$ dollars, then I'll have twice as much money as he will have. How much money does my brother currently have (in dollars)?
Let's say that my brother currently has $x$ dollars.
When I give him 5 dollars, he will have $x + 5$ dollars and I will have $x - 5$ dollars.
If we have the same amount of money, then $x + 5 = x - 5$.
Simplifying the equation, we get $10 = -10$, which is not true.
So, this case is not possible.
Let's consider the other situation.
If my brother gives me 10 dollars, he will have $x - 10$ dollars and I will have $x + 10$ dollars.
If I have twice as much money as him, then $x + 10 = 2(x - 10)$.
Expanding the equation, we get $x + 10 = 2x - 20$.
Subtracting $x$ from both sides, we get $10 = x - 20$.
Adding 20 to both sides, we get $30 = x$.
Therefore, my brother currently has $\boxed{30}$ dollars. Answer: \boxed{30}.