Although the All Writs Act isn't an independent basis for jurisdiction, Mandamus against unreasonable administrative delay validly runs from the Circuit Courts when necessary to protect their future jurisdiction.
Mandamus against delay by the Dept of Veterans Affairs should be governed not by a finding of the official's refusal to act, but by a common-law balancing test.
Concur: An over five-year appeals process, mostly composed of ministerial tasks and docketing, is excessive. Mandamus is the only viable option.
http://www.cafc.uscourts.gov/sites/default/files/opinions-orders/17-1747.Opinion.6-5-2018.1.pdf
Since 2011. An occasional commonplacing of the U.S. Circuit Courts of Appeal.
Neither an authoritative statement of the law nor legal advice. Quick work.