What is the range(distance) for remote access for normal routers like belkin?
What model router exactly? A Belkin router that supports only 802.11g has a shorter range than one that supports 802.11n. And... there are differences in the implementation of the 802.11 protocol as well (Single antenna versus Dual antenna versus Triple antenna, MIMO, etc.). Otherwise, figure about 600 feet.
Can someone from over 5 miles connect to the router if remote access is enabled?
Yes. But not for any reason you are thinking of. Remote Access means that your router can be accessed by going to your external IP address. If Remote Access is disabled, then no matter what, unless someone is on LAN, they can't access the Admin panel of the router. If you enable Remote Access, then you no longer have to only be on your LAN to access the Admin panel. Anyone with your external IP address can then visit the initial Belkin info page... and if you didn't change the password from factory default, they can then easily access your router's settings. Remote Access has NOTHING WHATSOEVER to do with wireless range or wireless access.
What about port forwarding?
What about it? Are you asking what it is? Are you asking how to configure it? Are you asking if using it means someone at some odd range can access your computer? What EXACTLY are you asking about port forwarding?
EDIT addressing your comments. No. If you forwarded specific ports to an internal IP address (a computer) on your LAN, then someone could not sneak in piggybacked on that port, and enable Remote Access on your router. If they could, they would not NEED to enable Remote Access, as they would already obviously have it somehow.
Even if someone finds an open port, and connects to your laptop, can they go through your router settings and connect to your connection? No. Your laptop is not set by default to share your connection in any way. More importantly, if your laptop was then set to use ICS (internet connection sharing) it could only share an internet connection over a DIFFERENT network connection... meaning if your laptop that connects to the router via it's wireless card, could only share an internet connection to a computer that was connected to it's wired ethernet port... not back over the same wireless.
I suspect you still haven't expressed what you mean, however... and I expect more comments will be forthcoming that will further pare down what it is exactly that you need to know. However, I'm going to add some preemptive information here.
It would be far easier to hack your wireless security to connect to your router, than anything you are currently attempting to suggest. That's right. All someone would need to do is guess or hack your wireless security passcode, and they would be connected just like any other computer on your network. I'm not saying that it is easy to do this. I'm saying that it is EASIER to do this, than it is to do anything you are suggesting or hinting at. Remote access does not mean that someone at a remote location can use your internet connection. Remote access means that someone OUTSIDE of your local area network could access the router administration settings.