To have five 3-piece sets, he needs to have a total of 5*3=<<5*3=15>>15 shoes,
If he already owns three shoes, then he needs to buy 15-3=<<15-3=12>>12 additional shoes.
Since each pair of shoes includes two shoes, he needs to buy a total of 12/2=<<12/2=6>>6 pairs of shoes.
#### 6