For nuclei which have a nuclear spin of 5/2 and exhibit a small asymmetry parameter of the electric field gradient (77) at the nuclear site, line shapes of the Powder Zeeman NQR (PZNQR) spectra based on the transition between the energy levels m x = ± 1/2 and ± 3/2 (the lower frequency line) were studied by means of computer simulations and experiments, (i) When an 77 value is very small (type 1; 77 = 0), the line shape exhibits two shoulders like the style of the American football player, (ii) While an 77 value is small (type 2; 0< 77 < around 0.01) but not zero, the line shape has two small peaks which are symmetrically located on the shoulders, as in the case of the small 77 type of spin 3/2. (iii) When an 77 value is not small (type 3; around 0.01 <77), the line shape has two symmetrical dips in stead of the peaks, which are also similar to the case of not small 77 type of spin 3/2. As the 77 value increases from around 0.01, the two dips grow and reach the maximum at the 77 value of 0.349, and then become smaller and obscure in the range of 77 larger than 0.