Usually it's bad valve-stem oil seals but could also be rings in engines that are in really bad shape. It could also be the PCV line if the PCV valve is stuck or you overfill. Then there are leaks.
Base oil burns and gets out of the exhaust but some of it becomes varnish and gunk. On top of that the metal additives (detergents, moly, etc.) don't burn and form oil ash. Some of the oil ash permanently remains in the cylinders and on the spark plugs. Also, some additives, especially ZDDP, are poisonous to the oxygen sensor and catalyst, and reduce their lives. With diesel particular filters (DPF), ash going through the exhaust end up being caught in the DPF, eventually helping to clog it. For that reason, for DPFs, they require newly introduced low-SAPS oils (ACEA Cx categories) that are not readily available in US as there are few diesels here.
1 qt in 5k miles is a little high but not bad at all. I would have liked it to be less than 1 qt in 10k miles, but hey, everything in life experiences wear and tear and therefore slowly but constantly ages.