We present an analysis of a 40 ksec Chandra observation of the galaxy group AWM 5 . It has a small ( \sim 8 kpc ) dense cool core with a temperature of \sim 1.2 keV and the temperature profile decreases at larger radii , from \sim 3.5 keV just outside the core to \sim 2 keV at \sim 300 kpc from the center . The abundance distribution shows a “ hole ” in the central \sim 10 kpc , where the temperature declines sharply . An abundance of at least a few times solar is observed \sim 15 - 20 kpc from the center . The deprojected electron density profile shows a break in slope at \sim 13 kpc and can be fit by two \beta -models , with \beta = 0.72 _ { -0.11 } ^ { +0.16 } and r _ { c } = 5.7 _ { -1.5 } ^ { +1.8 } kpc , for the inner part , and \beta = 0.34 \pm 0.01 and r _ { c } = 31.3 _ { -5.5 } ^ { +5.8 } kpc , for the outer part . The mass fraction of hot gas is fairly flat in the center and increases for r > 30 kpc up to a maximum of \sim 6.5 \% at r \sim 380 kpc . The gas cooling time within the central 30 kpc is smaller than a Hubble time , although the temperature only declines in the central \sim 8 kpc region . This discrepancy suggests that an existing cooling core has been partially re-heated . In particular , thermal conduction could have been a significant source of re-heating . In order for heating due to conduction to balance cooling due to emission of X-rays , the conductivity must be suppressed by a large factor ( at least \sim 100 ) . Past AGN activity ( still visible as a radio source in the center of the group ) is however the most likely source that re-heated the central regions of AWM 5 . We also studied the properties of the ram pressure stripped tail in the group member NGC 6265 . This galaxy is moving at M \approx 3.4 _ { -0.6 } ^ { +0.5 } ( v \sim 2300 km s ^ { -1 } ) through the hot group gas . The physical length of the tail is \sim 42 kpc and its mass is 2.1 \pm 0.2 \times 10 ^ { 9 } M _ { \odot } .