Solution:

"Let x be my present age. My age 2 years from now will be x + 2, and 2 times that will be 2 (x + 2). Similarly, my age 3 years from now will be x + 3, and 3 times that will be 3 (x + 3).

Adding the two gives 6 times my current age. This gives the equation:

2 (x + 2) + 3 (x + 3) = 6 x.

Solving the above equation gives

x = (2 × 2) + (3 × 3) = 13.

Thus, I will be 18 years old 5 years from now."

Food for thought:

How do you verify the answer?
It's easy! By substitution, right?