(Abridged) WASP-5b is a highly irradiated dense hot Jupiter orbiting a G4V star every 1.6 days. We observed two secondary eclipses of WASP-5b in the J, H and K bands simultaneously. Thermal emission of WASP-5b is detected in the J and K bands. The retrieved planet-to-star flux ratios in the J and K bands are 0.168 +0.050/-0.052% and 0.269+/-0.062%, corresponding to brightness temperatures of 2996 +212/-261K and 2890 +246/-269K, respectively. No thermal emission is detected in the H band, with a 3-sigma upper limit of 0.166%, corresponding to a maximum temperature of 2779K. On the whole, our J, H, K results can be explained by a roughly isothermal temperature profile of ~2700K in the deep layers of the planetary dayside atmosphere that are probed at these wavelengths. Together with Spitzer observations, which probe higher layers that are found to be at ~1900K, a temperature inversion is ruled out in the range of pressures probed by the combined data set. While an oxygen-rich model is unable to explain all the data, a carbon-rich model provides a reasonable fit but violates energy balance.
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