Help! When exactly did Giles buy the shop? My mind has gone blank.

I think it was in "Real Me," when they found out the previous owner was dead, Giles decided to buy it.

Tammy, you rule! I could picture it in my head but could not place it in Season 5. Yay! Thanks very much.

No problem, I just remembered that it was when Dawn showed up.

It was Harmony's gang that killed the previous owner.  Giles figures it out when they discover that a unicorn is missing from the inventory, I believe.  Giles is looking through the books and marvels at the profit margins :-)