First, order the data:
5, 5, 6, 6, 7, 7, 7, 8, 8, 8, 8, 9, 9, 9, 10.
The median (Q2) is the 8th datum: 8.
We now have a dataset split into two halves: 5, 5, 6, 6, 7, 7, 7 and 8, 8, 8, 9, 9, 9, 10.
Now take the central datum of each half: 6 (Q1) and 9 (Q3).
The IQR is 9-6=3.