A simple way you could solve this is by drawing a tape graph.
Draw a long rectangular box.
Cut the box into 8 pieces, seeing as how 5/8 of the coins are dimes.
We have to take 48 and divide it by 8, we get 6, so now we know how many dimes are evenly split into each piece.
Now color in 5 pieces of the tape.
This represents the 5 in 5/8.
Now to find the number of coins, simply multiply 5 by 6, you get the answer of 30.
I hope this helps, if you are confused with any part of my explanation, ask and I will clarify.