Abstract For nuclei which have a nuclear spin of 5/2 and exhibit a small asymmetry parameter of the electric field gradient (ƞ) at the nuclear site, line shapes of the Powder Zeeman NQR (PZNQR) spectra based on the transition between the energy levels m1 = ± 1/2 and ± 3/2 (the lower frequency line) were studied by means of computer simulations and experiments. (i) When an ƞvalue is very small (type 1; ƞ= 0), the line shape exhibits two shoulders like the style of the American football player. (ii) While an ƞvalue is small (type 2; 0 < ƞ< 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 ƞtype of spin 3/2. (iii) When an ƞvalue is not small (type 3; around 0.01 < ƞ), the line shape has two symmetrical dips in stead of the peaks, which are also similar to the case of not small ƞ type of spin 3/2. As the ƞvalue increases from around 0.01, the two dips grow and reach the maximum at the ƞvalue of 0.349, and then become smaller and obscure in the range of ƞlarger than 0.349.The observations of PZNQR spectra were performed for several compounds including the 127I and/or 121Sb nuclei to estimate the ƞvalues, and gave the results as follows: very small for 127I (207.683 and 209.133 MHz, at 77 K) in Snl4; very small for 127I (176.496 and 177.438 MHz, at 77 K) in Gal3; small for 127I (265.102 MHz, at 77 K) in CH3I; 0.33 for 127I (247.69 MHz, at 77 K) in C2H5I; 0.27 for 121Sb (58.23 MHz, at 290 K) in SbCl3. The estimated ƞvalues 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 ƞ, though somewhat large disagreements were seen in the cases of not small ƞvalues.