We herein report a copper-catalyzed formal [5 + 2] aza-annulation of N-fluorosulfonamides and 1,3-dienes/1,3-enynes for synthesis of structurally diverse alkene/alkyne-containing azepanes. The reaction features selective functionalization of distal unactivated C(sp3)–H bonds and a broad substrate scope, thus allowing the late-stage modification of pharmaceuticals and natural products. A radical mechanism involving 1,5-hydrogen atom transfer of N-radicals, facile coupling of alkyl radicals with 1,3-dienes/1,3-enynes, and the construction of azepane motifs via C–N bond formation is proposed.