The ratio 5:3 means that one person has 5 parts, the other has 3 parts.
The first thing to work out is the total number of parts. In this case, it is 5+3 = 8.
Next work out the value of each part. You have to divide 16, so the value for each part is 16/8 = 2.
For the two people (or whatever), one person has 5 parts = 5 * 2 = 10. The other has 3 parts = 3 * 2 = 6.
So you answer is 10 and 6.
I hope that explains it well enough for you.