Where does the requirement say that those 5 years (60 months) after the age of 16 have to be accumulated between the age of 16 and 21? (22 actually)
You said: “Did Obama’s mother live in the USA for a grand total of least 5 years (60 months) after she turned 16?”
Yes, but not before Barack was born when she was 18, which is the only time-frame that matters for purpose of determining his citizenship.
You said: “Where does the requirement say that those 5 years (60 months) after the age of 16 have to be accumulated between the age of 16 and 21? (22 actually)”
It doesn’t: what matters is the accumulated amount of time, but unless the required amount occurs before the child is born, such a mother cannot confer citizenship on her child. In Obama’s case, his mom fell far short of this requirement.
“When enacted in 1952, section 301 required a U.S. citizen married to an alien to have been physically present in the United States for ten years, including five after
reaching the age of fourteen, to transmit citizenship to foreign-born children. The ten-year transmission requirement remained in effect from 12:01 a.m. EDT December 24, 1952, through midnight November 13, 1986, and still is applicable to persons born during that period.”
http://www.state.gov/documents/organization/86757.pdf
The above document has great gobs of detail about the exact requirements, who has to prove what and how etc., what counts as “physical presence” etc., what happens if American mom is unwed etc.