A close friend will graduate university in the US with a degree and wants to be part of a faith based medical outreach before the start of medical school 5 months months later.

What is the best way to accomplish this? Multiple entry (90 day) with an extension, or 60 day tourist visa that is extended? Jan of 2017 through May 2017.

He should first secure a "job" offer from an organisation which will provide the paperwork needed to secure a visa and the necessary Work Permit.

I'm not following. He wants to stay 5 months in Thailand and do what exactly here? And after 5 months he will be back to the US?

This all depends whether the faith-based medical outreach group routinely has medical school student volunteers in Thailand or the friend would be their first one.

a multi entry tourist visa (metv) will do up to 9 months with extensions, as long as there is no work involved,

a 90 day non immigrant visa stamp, can not be extended unless married to a thai national.

a 60 day tourist visa stamp can only be extended once for 30 days , unless married to a thai national

Best would be METV. Two back to back setv with extension would give 6 month. One setv followed by stamp with extensions 5. However cannot work or do volunteer work. Not completely clear what your friend intends to do in Thailand.