I drive a 2011 Tundra 5.7 with TRD Supercharger approx 510hp / 550tq.
Initially my first oil change they used conventional as this is what is recommended 5w/20.
5.7L V8 (3UR-FE, 3UR-FBE) engine
Oil grade: ILSAC multigrade engine oil
Recommended viscosity: SAE 5W-20 or 0W-20
SAE 5W-20 or 0W-20 engine oil
may be used. However, SAE
0W-20 is the best choice for
good fuel economy and good
starting in cold weather.
I agree with others that the Mobil 1 0W-40 European Formula is a wise oil choice. A mix including a quart or two of 15W-50 may be better because of its resistance to shear forces and its ability to remain on the metal components after shutdown. The suggestion to use M1 5W-40 Turbo Truck is a good one because that oil has ester in it as well as PAO. See Material data Sheet.
The Germans make great cars and they do not recommend 0W-20 but 0W-40 instead. I think the German manufacturers have got it right.
Mobil recommends 0W-40 and 15W-50 for "street racers" and applications that involve heavy hauling up long grades. The start value of 0W-20 cannot be argued, but I have noticed that engines using oil that light have more valve train noise than engines using a bit higher grade on the second number. 0W-20 would be fine if you never tromp on the throttle or push the motor, IMO.
Here is a quote from Mobil on their 15W-50. They're talking about your truck.
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Mobil 1 15W-50 Mobil 1 15W-50
Mobil 1 15W-50 is an advanced full synthetic motor oil designed to help provide exceptional wear protection for a smooth driving experience.
Mobil 1 15W-50
Mobil 1 15W-50 meets or exceeds the requirements of the industry and car manufacturers’ standards required for high-performance turbo-charged, supercharged gasoline and diesel multi-valve fuel-injected engines. Mobil 1 15W-50 is a winning, race-proven technology. It is especially suited for a wide variety of motorsports applications, towing and other severe service situations. Mobil 1 15W-50 synthetic motor oil helps provide outstanding motor oil performance and protection for the winning edge. Mobil 1 is the official motor oil of NASCAR®
For every day, 0W-40 and for the days doing serious hauling, a quart or two of 15W-50 would act real nice in the sump.