Let's use variables to represent the amounts of money each person has. Let's say Raina has x dollars.
According to the information given, Henry has $5 more than Raina, so Henry has x + $5.
Sam has 2 times what Henry has, so Sam has 2(x + $5) = 2x + $10.
The total amount of money they have is $71, so we can create an equation: x + (x + $5) + (2x + $10) = $71.
Simplifying the equation, we have 4x + $15 = $71.
Subtracting $15 from both sides, we get 4x = $56.
Dividing both sides by 4, we find x = $14.
Therefore, Raina has $14, Henry has $14 + $5 = $19, and Sam has 2($19) + $10 = $48.
So Raina has $14, Henry has $19, and Sam has $48.