The water temp is too high... it should be between 72-72F. Since it is close to the basking temp (which is fine), this could be contributing to him not basking as well as the fact he is new. Try lowering the water temp. If you have a heater in there, turn it down. If this is from warmer weather, you can try doing partial water changes with cool water, or dropping in either ice cubes or frozen bottles of water.
Also, look into upgrading his home ASAP. Minimum tank size should be 10 gallons per inch of shell with as much water as you can fill it without giving them room to escape. A full grown RES will need at least 90-120 gallons, so go as large as possible now to save yourself money in the long run.
