You have received a lot of good advice so far. Here are some additional things to consider.
Why is the current owner selling it so so soon. Was it redundant before?
Did they buy something else that made it redundant, why?
My newish rule on buying used is look it over very carefully. Figure out what it needs to make it good enough for who it's for. Add 20 to 30% of the purchase cost for unforseen issues and expect to spend at least a couple of months of weekends dealing with these issues. If it still feels like a good deal, then it probably is.
I did this on my X749 and bought it anyway. Here is what I didn't notice or broke soon after:
1. Tilt steering wheel is very loose in tilt direction, almost a full notch worth.
2. Makes a grinding scraping sound from front axle/wheels.
3. Transaxle frame mounts are cracked
4. Appeared radiator was leaking, but just turned out it was the hose, so replaced the hoses and fan belt, which was almost broken.
5. There was a loud clunk in the steering. Traced this to the middle control arm, which is the cheapest one. Others probably could use replacement, but are still working.
I did notice the following before buying:
1. The tires are old, but still working.
2. The left rear taillight is held on by electrical tape.
3. There was lots of condensation in the dash.
4. It has 1300+ hours, so expected it would need some time and dollars to get to good enough.
Every used piece of equipment I have purchased in the last couple of years has needed more than I expected going in. I am still glad I bought all of them, but I made sure the price I paid was consistent with the condition being much worse than I expected. I also knew that it would take me some time to figure out the majority of the issues. I am still working through that on the X749 months later. I have spent way more time working on it than actually using it and I am not done with getting it to good enough.
The X585 is a very nice machine. They are generally reliable. Parts are generally available, but they are very expensive, but that is the case for most things Deere. I didn't want to spend the $ for a new X739, since I wasn't sure I would like it well enough for the $. The X749 was a test. I figured if I didn't like it, I could sell it for not too much of a loss. It also meant I could keep my X534 for mowing. I am glad that I made that decision. I think the X749 is too big and too top heavy (not that it is that top heavy) for certain areas of my property that are very challenging. So, if your primary reason for getting the X585 is mowing, make VERY sure it really will be a better mower than what you have. In some respects, my X300 is the best mower of the three I have. The X534 has a lot things that make it easier and more comfortable, but it doesn't really mow better.