Have the dealer run the SN to determine that all recalls (e.g., TPS) are done. Make sure the CCT Is fresh. And the one thing I'd really hope for: that the bike was diagnosed as a ticker and fixed.
Read up on Gen.I exhaust valves "ticking". The OEM exhaust valve guides resulted in erosion in a small percentage of 2003 - 2005 FJRs. After Warchild and others here got their attention by documenting the problem, Yamaha stepped up and did head jobs with new exhaust valve guides for $0, even when out of warranty (in USA at least, and back a while). The tick could occur after a few thousand miles, a few tens of thousands, or not at all. Mine was around 23,000 miles and fixed around 29,000.
If a tick occurred and it was fixed, you have the gold standard. If it never was diagnosed, make sure it isn't ticking and hope that the odds mean that you have a non-ticker well into the future.
Also make sure the ABS cycles for the front and rear brake. The dealer can jumper it to activate, or you can take it out into a dirt parking lot and hard stop one wheel at a time from a slow roll (without dumping it!). Have the dealer replace brake fluid in the cylinders, lines, ABS block and clutch. Lastly, make sure the first required valve check was done (@~26,000 mile), and that adjustment isn't required now. Make sure that the spark plugs, oil, filters and gear lube are fresh or within spec.
Otherwise - the 2005 is pretty free of problems and a lot of bike for what price they bring nowadays. Good luck - that bike very well could be good for another 150,000+ miles.