I'm a 29 year old female & pretty healthy overall. Taking birth control for 5 years- what's the risk of deep vein thrombosis or serious blood clot?

Birth control. There certainly is a relationship between use of contraceptives, either orally or even in an IUD, and potential venous thrombosis. I would discuss this issue with her gynecologist as almost all of the birth control pills have been implicated in causing a venous thrombosis. Also with airplane travel that may increase the risk, and I would recommend use of a support stocking during airplane travel.
Depends. The risk with birth control pills is higher than without, but much lower than the risk with pregnancy. The risk is higher in overweight women and those who smoke. A small number with a genetic mutation have excessive risk. Regular exercise will reduce the risk. See this site for more info. http://www.webmd.com/sex/birth-control/tc/hormonal-birth-control-risk-of-blood-clots-topic-overview.
Clots. Birth control pills can certainly increase the risk for deep vein thrombosis although the current low estrogen BCP's do not increase the risk that much. If you had a tendency for female hormonal related blood clots it would certainly have appeared in the first one to two years on BCP's. If is unlikely you will have serious blood clots after five years.