Numerical simulations are performed for the flow around an inclined 5:2 prolate spheroid in a uniform freestream. The Reynolds number (Re=300, 500, 700, and 1000) and incidence angle (alpha = 0 degrees-90 degrees) are considered as significant parameters affecting the wake transitions, where alpha = 0 degrees indicates flow parallel to the major axis of the prolate spheroid, and the Re is based on the inflow velocity U-0 and the volume-equivalent sphere diameter D-e of the spheroid. In the range considered of Re and alpha, eight flow regimes are identified: (i) steady axisymmetric (SA) flow regime; (ii) steady planar symmetric flow regime; (iii) steady asymmetric (SAS) flow regime; (iv) periodic planar symmetric flow regime with non-zero mean lift or "Zig-zig-like" (Zz-like) mode; (v) periodic asymmetric flow regime with double-sided vortex shedding; (vi) multi-periodic asymmetric flow regime with double-sided vortex shedding and low frequency modulation (MPADL); (vii) multi-periodic asymmetric flow regime with single-sided vortex shedding and low frequency modulation (MPASL); and (viii) weakly chaotic state. Three of them are new and first reported, i.e., SAS, MPADL, and MPASL modes. The wake structure of the Zz-like mode is different from that of the zig-zig mode in the sphere/disk wake with a pair of streamwise vortices extending to the near wake. It is found that the elongated body can delay the onset of unsteadiness at small incidence angles. A flow regime map in the considered (Re, alpha) space is then provided. Finally, the physical mechanisms of the low-frequency phenomena observed at different wake modes are explored. Published under an exclusive license by AIP Publishing.