Would it be better to use synthetic oil in my 2004 F250 6.0 diesel? If so should I use 5W40 or 15W40?
Thank you

You absolutely want to use full-synthetic heavy duty diesel engine oil (HDDO) in your truck, especially if it has a turbo. I would lean towards SAE 5W-40 for slightly better mileage.

These links may help:

https://www.askmehelpdesk.com/cars-trucks/faq-how-troubleshoot-repair-maintain-hondas-selected-other-vehicles-46563-8.html#post1415281

https://www.askmehelpdesk.com/cars-trucks/faq-how-troubleshoot-repair-maintain-hondas-selected-other-vehicles-46563-12.html#post2162069