Right there in your owner's manual. This may not be the correct procedure for your F525 as you didn't post a serial number.

If you don't have a manual they can be read and bought on the JD web site.

thanks for the advice however my mower is a 1997 front mower where those tires are at the front not back . at the back middle is a smaller tire for steering. I
would feel very dumb if I couldn't change the tire in the pic you sent. my owners manual doesn't show anything

I can not help from experience but you may get help at the John Deere Parts site (all one string.)
http://jdpc.deere.com/jdpc/servlet/com.deere.u90490.partscatalog.view.servlets.HomePageServlet_Alt

Enter f525 in the little box in the upper left of the screen. This will bring up a parts diagram for the f525 mower with a parts list.

It looks like there are five wheels on the mower if I got the model number correct.

The instructions JAL posted were correct - I think the difference is that the F510 came with a 38" deck and the F525 is 48"

Looks to me like you have to remove the deck - instructions in the link knuttle provided, or

Here is a link that might be useful: Deck removal F510/F525

I have never worked on a 510 or a 525, so this is probably a dumb comment.
Does that deck "articulate" (pivot) like a hinge where it attaches to the tractor?
If so, maybe you could use a jack on the front of the deck to raise it, and that might allow the deck trailing (anti scalp) wheel on the deck to swing enough out of the way for the tire to miss it.
Could the trailing wheel be removed without taking the deck off?
If so, even that little bit of extra clearance may be helpful.
I scanned through the owner's manual and found it to be devoid of any useful tips on this specific issue.

I had to change the same tire a few weeks ago. The deck will have to be disconnected.

First remove the deck belt.

Attached is a photo showing the pins to be removed in numbered order.

1) Disconnect the pin that attaches the lift cable to the deck.

2) Disconnect the long pin located under the mower. It goes through the yellow arm and the left main arm of the deck. I had to use a long punch to remove mine. A 1/4" socket extension would probably work.

3) Remove the pin from the right arm.

4) Remove the pin from the left arm.

Slide the deck out, jack up the mower and remove the tire.

Adam, it doesn't get much more straightforward than your photo with arrow indicators. Good job..

Thanks, I have to do stuff like this pretty often with my job.