15 years ago, Shyam was twice as old as Prabhat. Five years from now Prabhat’s age will be $$\dfrac{5}{8}th$$ of Shyam’s age. What is Shyam’s current age?

Let the present age of Prabhat be P years and that of Shyam be S years.
Age of Prabhat and Shyam 15 years ago will be P - 15 years and S-15 years respectively.
Given, $$S-15 = 2 \times (P-15)$$
=> S - 15 = 2P - 30
=> 2P - S = 15
=> 2P = S+15
=> P = $$\dfrac{S+15}{2}$$

Ages of Prabhat and Shyam 5 years hence will be P+5 years and S+5 years respectively.
Given, $$P+5 = \dfrac{5}{8} \times (S+5)$$
=> 8P+40 = 5S+25
=> 5S - 8P = 15
Substituting P = $$\dfrac{S+15}{2}$$ in above equation
$$5S - 8 \times (\dfrac{S+15}{2}) = 15$$

=> 5S - 4S - 60 = 15
=> S = 75
Therefore, The present age of Shyam is 75 years.