Channel 5's analogue transmissions are generally at a much lower power than the other four analogue channels. (Channel 5 was 'squeezed in' in a way that meant that full-power transmissions might cause interference to other broadcasters). Additionally, different makes of TV have differing 'sensitivities' (i.e. the ability to lock onto, and resolve, weak signals).
Your new TV has got a poorer sensitivity than your old one - assuming, of course that your old one received Channel 5. You need to increase the signal strength. If your old TV received C5 OK, you'll probably be able to get the required signal strength by simply adding a cheap signal booster. However, if you've never had good C5 reception, you might need to upgrade your aerial (or switch to digital reception).
That answer assumes that your TV is an analogue model (i.e. without built-in Freeview reception). However, even if your TV is a digital model, the problem is still almost certainly related to insufficient signal strength.
Chris