Well in 17 years and that many kilometers, there are dozens of things that could have gone wrong due to accident, bad driving, flood, misadventure or neglect. So you have to check/have checked everything.

But it's a a pretty robust and reliable model and year - here's some of the more frequent problems

https://repairpal.com/2005-toyota-avalon/problems

Two main issues with this generation:

1- Oil leak from front time cover and valve cover gasket. 

2- Power steering rack leak.

They’re about as good as 17 year old 150,000 mile cars get.

Awesome GR engines, continue to be some of Toyota’s best.

I’d recommended the simpler 5 speed over the 6 speed. The 6 was never really that good.

Good car, but old and a bit too much mileage.

I’d try to find one with around 90k~100k miles and closer to ~2010 just to play it safe.

But if you can’t find any / alternatives are too expensive - it can be alright.

As always, have it checked out by a mechanic to make sure there isn’t anything seriously wrong with it.