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We present the results of Suzaku and Chandra observations of the galaxycluster RXC J1053.7+5453 ($z=0.0704$), which contains a radio relic. The radiorelic is located at the distance of $\sim 540$ kpc from the X-ray peak towardthe west. We measured the temperature of this cluster for the first time. Theresultant temperature in the center is $ \sim 1.3$ keV, which is lower than thevalue expected from the X-ray luminosity - temperature and the velocitydispersion - temperature relation. Though we did not find a significanttemperature jump at the outer edge of the relic, our results suggest that thetemperature decreases outward across the relic. Assuming the existence of theshock at the relic, its Mach number becomes $M \simeq 1.4 $. A possible spatialvariation of Mach number along the relic is suggested. Additionally, a sharpsurface brightness edge is found at the distance of $\sim 160$ kpc from theX-ray peak toward the west in the Chandra image. We performed X-ray spectraland surface brightness analyses around the edge with Suzaku and Chandra data,respectively. The obtained surface brightness and temperature profiles suggestthat this edge is not a shock but likely a cold front. Alternatively, it cannotbe ruled out that thermal pressure is really discontinuous across the edge. Inthis case, if the pressure across the surface brightness edge is inequilibrium, other forms of pressure sources, such as cosmic-rays, arenecessary. We searched for the non-thermal inverse Compton component in therelic region. Assuming the photon index $ \Gamma = 2.0$, the resultant upperlimit of the flux is $1.9 \times 10^{-14} {\rm erg \ s^{-1} \ cm^{-2}}$ for$4.50 \times 10^{-3} {\rm \ deg^{2}}$ area in the 0.3-10 keV band, whichimplies that the lower limit of magnetic field strength becomes $ 0.7 {\rm \\mu G}$.

Suzaku and Chandra observations of the galaxy cluster RXC J1053.7+5453 with a radio relic