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3rd Gen Ram Tech2002-2008 Rams: This section is for TECHNICAL discussions only, that involve the 2002 through 2008 Rams Rams. For any non-tech discussions, please direct your attention to the "General discussion/NON-tech" sub sections.
It's one step up in tire height, you'll be fine, just a taller sidewall. 02-03 the stock 20 was 275/55, then 2004 changed it to 275/60 well into the 4th gen run.
You might be pushing it at that height, the width is fine, if a bit bulgy on a factory 20x9 wheel. The 275/65 is only about an inch taller than the 275/60, but the 285/65 is a little over an inch and half taller than the 275/60. Assuming you have stock 20's with the stock size 275/60's on it, you need to turn it to full lock, add 3/4" past the tire and see if that's gonna hit anything.