B is for battery. Make sure all connections are clean and tight. How old is machine? How old is battery? Was it starting OK with that battery recently? 5 year life if your lucky in my experience. You can take it out and have it load tested or use any good battery to crank the engine but make sure you have correct polarity and good connections with test battery.

Tractor and battery are about 5 years old. All connections are tight. It started fine in the Fall, but off course was not used over the winter. I'll take it out and get it load tested.

B

That recorded sound is a bit "inconclusive", but I will venture to say it is either due to the rapid activate/deactivate cycling of the starting relay (the solenoid) because of a low and "borderline dead" battery...........OR else, the starter drive pinion gear or the flywheel gear teeth are sheared off.
The easiest way to determine if the battery is the culprit is to "boost" or jump start the machine using another vehicle and jumper cables. If the machine refuses to start with a boost, and still makes the noise, you need to double check ALL the connections of the battery cables, not just at the battery but anywhere either of the cables has a connecting point to the frame, the engine, the solenoid, the starter.........ALL connections are equally important.
If you find nothing wrong in the way the cables are connected, then, you can concentrate on the starter itself.

Your machine won't start and the battery is 5 years old? I think you answered your own question. BTW, its quite common for a battery to show 'good' with a vold meter yet under load is dead as a door nail. This is why they have load testers. IOW, a tester that will simulate a load when it reads to you the voltage. This is a real test. What you did proved virtually nothing. 5 yr old battery + 1 yr on the selling floor before you bought it, that's 6 years! That battery is Dead.

OP here. As most suspected the battery was the culprit. Replaced it and the tractor runs fine. Thanks everyone for the help.