If it is cold when you first start it, and that is when it runs for 5 minutes, it is most likely a carburetor problem. What usually happens is you get a vaccuum leak or you pick up some sediment in the carb bowls.
The reason it may run for 5 minutes when cold, is that the choke and fast idle are on then, and it is enough to keep it running, once the fast idle kicks down to normal idle RPM range, it will stall. Will it stay running when you rev it? If so, this is most likely the problem.
If so, check your vaccuum hoses and fittings for leaks, especially any that are near the exhaust manifold, they deteriorate quicker than elsewhere from the heat. If no problems there, then check your fuel bowl for sediment, if there is any dirt at all, rebuild your carburetor, and that will most likely fix it.
One important thing to consider: The carb body is known to wear at the place where the trottle rod passes thru, and that can cause a vaccuum leak, most rebuild kits do not provide the bushing to replace there. Sometimes a new rebuilt carburetor is your best bet. Auto Zone carries Holley and one other brand, for roughly $250.
Or you could upgrade to a Weber, they are nice but about $460!!!