I put gas in tank (no matter what amount) car runs rough for 5 mi

Here is an idea.
It sort of sounds like there is a blockage after a while in the gas tank.
If there were sediment in the bottom of the gas tank, it would start and run fine sitting still.
However, when driving it, it would be a matter of a few minutes until the sloshing of the fuel would cause the sediment to mix in with the fuel, and clog the filter screen in the fuel tank.
When it stops, the sediment would settle back down, and in 15 - 20 minutes, it would be clear again.
God bless your efforts.

this is one that will need to be taken in for diagnostics, It is an EVAP System problem.. there are a few test that will need to be performed to help identify the probem.. a smoke test will be very useful here

NEADS A TUNE UP,ALSO PUT SOME INJECTOR CLEANER IN YOUR GAS TANK FIRST

fuel filter is bad or you have a dirty fuel tank go to auto zone get a bottle of sea foam and thats the name on the bottle fill your gas tank up to half a tank and pour the sea foam in the gas tank then drive it until you have refill it again now it will run rough after you put this in what its doing is breaking down all the trash and particules in the bottom of the gas tank and its clogging the filter after you do this replace the fuel filter and either way your solving the problem

• This will happen to a lot of people as the weather begins to cool. I suggest making sure you get gas from a reputable service station for one. Just as important make sure to put a bottle of HEAT in your tank with every fill up(half a bottle for half a tank fill up on fuel).

• What happens is there is already a certain amount of water no matter where you get fuel from as the storage tanks have a lot of water in them. That alone with the colder weather makes for rough starts and at times poor running conditions in the colder months because water freezes and makes the gas hard to pass through to the injectors and greatly effecting the engine firing properly. Heat will dry this water up and make your fuel flow much easier and burn a little better too.

• Try this and you will notice a difference. Just about anyone will during the colder months.

• Hope this helps.
  

CHANGE FUEL FILTER AND CHECK FUEL PRESSURE.SOUND LIKE FUEL PUMP FAILING OR FUEL PUMP RELAY BAD.

Try taking the exhaust pipe loose at the manifold. I had a Chevy Suburban that acted the same way, it turned out to plugged catyletic converter. The converter wasn't letting the exhaust out, the truck had no power, it would stall and then start right up and great for about five seconds the run rough and quit. Once I disconnected the exhaust it started right up and ran great. You could also try taking the O2 sensors out (for test purposes) ahead of the converter that will give the exhaust a place to go

Turn the key to full power (but do not crank the engine). You may hear a high pitched whine from behind you - that's the fuel pump running. Leave the key on for about five seconds, then turn it off for a minute. Turn the key on again for another five seconds, and off for a minute. Then turn the key on for five seconds, and then crank the engine.

If your car ran out of gas, you need to run the fuel pump this way to get fuel up to the engine again - all the lines from the tank to the engine are empty, so the pump needs to run to fill them.

If this doesn't work, it's possible that the fuel pump is vapor-locked and will have to be replaced. Some cars are more susceptible than others to this type of failure.

Sounds like you could have gotten some water in your fuel tank from that fill up. Go to a autoparts store and get a product to put in the tank that takes care of water in fuel. Use it when you fill the tank up a few times after and hopefully it goes away. Whenever you can't sustain power in the engine or it runs rough then your cruise control will constantly be shut off because the engine doesn't have the power to keep the speed up and should go away once your engine is running clean again.

Good Luck

Sounds like water in fuel tank. Try putting some gasline antifreeze in, (maybe a couple of bottles) will clear up water and problem if that's it.