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 mx = ± 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 0.349. _ The observations of PZNQR spectra were performed for several compounds including the , I and/or 1 2 'Sb nuclei to estimate the 77 values, and gave the results as follows: very small for I (207.683 and 209.133 MHz, at 77 K) in Snl4; very small for I (176.496 and 177.438 MHz, at 77 K) in Gal3; small for I (265.102 MHz, at 77 K) in CH3I; 0.33 for I (247.69 MHz, at 77 K) in C2H5I; 0.27 for Sb (58.23 MHz, at 290 K) in SbCl3. The estimated 77 values were compared to those obtained from the frequencies of two NQR lines for spin 5/2. They were in good agreement with each other for the small region of 77, though somewhat large disagreements were seen in the cases of not small 77 values.