We present an analysis of a 40 ksec Chandra observation of the galaxy group AWM 5. It has a small ($∼8$ kpc) dense cool core with a temperature of $∼1.2$ keV and the temperature profile decreases at larger radii, from $∼3.5$ keV just outside the core to $∼2$ keV at $∼300$ kpc from the center. The abundance distribution shows a "hole" in the central $∼10$ kpc, where the temperature declines sharply. An abundance of at least a few times solar is observed $∼15-20$ kpc from the center. The deprojected electron density profile shows a break in slope at $∼13$ kpc and can be fit by two $β$-models, with $β=0.72_-0.11^+0.16$ and $r_c=5.7_-1.5^+1.8$ kpc, for the inner part, and $β=0.34±0.01$ 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 $∼6.5%$ at $r∼380$ kpc. The gas cooling time within the central 30 kpc is smaller than a Hubble time, although the temperature only declines in the central $∼8$ 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 $∼100$). 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.