A　scheme　is　proposed　for　achieving　robust　population　inversion　in　five-level　systems　by　means　of　composite　pulses.　An　example　of　such　a　system　consists　of　the　magnetic　sublevels　with　angular　momenta　Jg=2$J_g=2$　and　Je=2$J_e=2$.　Through　elaborately　constructing　the　relative　phases　of　pulse　pairs,　the　composite　sequences　perform　well　in　suppressing　the　uncorrelated　pulse　area　errors.　In　particular,　the　five　pulse-pair　sequence　possesses　good　robustness　and　a　short　evolution　time.　The　composite　sequences　are　further　designed　to　compensate　for　a　single　type　of　pulse　area　errors　to　any　desired　order.　This　work　provides　a　high-efficiency　way　for　robust　quantum　state　manipulation　in　five-level　systems.　This　work　is　devoted　to　achieving　robust　population　inversion　in　a　five-level　quantum　system　by　means　of　composite　pulses.　The　designed　composite　sequence　can　compensate　the　pulse　area　errors　of　the　driving　fields　to　any　order.　The　results　demonstrate　that　the　proposed　method　is　promising　in　error-prone　environments,　a　superior　technique　for　high-fidelity　quantum　computation　in　multilevel　systems.　image