How long does it take for swelling to go down after having 5 teeth pulled?

Varies..: It depends how difficult the extractions were, how inflamed the tissue was before the extractions, and if you had an infection. The dentist/surgeon who extracted the teeth should be able to give you a more accurate answer.

Multiple extractions: is a surgical procedure and is not completely risk-free. Pain and swelling and bad taste following surgery is usually at its worst 24 – 48 hours after surgery. If you have undergone the tedious procedure of surgical extraction, these symptoms are common. If after 7 days no improvement, see your dentist or an oral surgeon for post-op appointment.