2005 Passat not running right consistently

The car starts perfectly. The first 3-5 miles down the road it runs perfect, then it doesn't have enough power to pull the hat off of your head. I've changed the air filter, no change. Changed the fuel filter, that got me 10 miles down the road, same problem. When it isn't running right I put a manual vacuum pump on the turbo, no change. On a different test drive, 3 miles into it, same thing again, I shut it off for 5 minutes, then it ran perfect again, but still acted up. It doesn't matter if its cold or warmed up. Do these cars have a transfer pump in the tank or some where else? It just seams to me that I"m not getting a constant flow of fuel to the filter/ injection system, thus when I first take off its fine and then it acts up.

Your advice is very welcomed.

pump number 1 is in the tank, pump number 2, Tandem, is at the back of the engine

OBD works, start there.

Are you seeing or smelling any fuel leaks?

No CEL and it resets on key off - key on? Sounds like turbo limp mode to me.

Even with the CEL off there is still likely fault codes stored. Scan it and go from there.

I'm sorry, I don't know what OBD and CEL stands for.
I did hook up a manual vacuum pump to the turbo actuator and that had no change when running poorly.

The very top google hit for OBD is "OnBoard Diagnostics" which is the correct context here.

CEL is the defunct but often still used term "Check Engine Light", which was pretty much universally changed to MIL or "Malfunction Indicator Lamp" over two decades ago.

Your car, like pretty much every other car on the road, employs computer control systems that allow for OBD. So does my dishwasher. It isn't exactly new. Started in the early 1980s on some models, but by the '90s most everything had it and by 1996 everything sold here that was for on road use HAD to have it. It is now in everything from agricultural equipment to fork trucks to the above mentioned household appliances.

Use it. Embrace it. It will make your life easier. That is what it is there for. We can guess all day.