Explanation

Cube both sides of a − 1/a = 5 using (u − v)³ = u³ − v³ − 3uv(u − v) with uv = 1: 125 = (a³ − 1/a³) − 3×5. Thus a³ − 1/a³ = 125 + 15 = 140, option (C). The common trap is answering 125 by forgetting the −3(a − 1/a) term.