Can I fix the slow channel-changing behavior on my TV?

I have an somewhat old TV (Sharp Aquos, Model # LC-32D40U) with basic cable from Time Warner. The cable runs straight from the wall to my TV, i.e., no cable box (Time Warner didn’t give me one since I just requested the bare bones cable tv package).

So here’s my problem: When I change channels, it is extremely slow to register the new channel. Usually takes about 5 seconds for the picture to register. Is there any equipment I can buy to remedy this?