5Mb download speed would be regarded as good by many people. (It's roughly what most people get in my road, although I get double that by having an ADSL2+ service).
Connectivity issues, such as the ones you refer to, most usually come about through interference on the channel used by your router. That can be caused by:
(a) your neighbours using routers on the same channel ; or
(b) the proximity of devices like printers (which emit loads of RF radiation) to your router.
Your new router will probably operate on a different channel to your old one, so your problem may well solve itself. Otherwise you'll need to access the router's settings to change the channel yourself. If you don't know how to do that (and you've lost the manual which tells you), we'll need to know the make of the router in order to assist you.
Chris