No need to hunt around for your John Deere 5515 from the 5015 series. Browse more than 190 parts here, including trailer couplings, lighting and electrics.
A tractor like the John Deere 5515 spends a lot of its life with something hitched behind it, so the rear end is a good place to start. This page lists more than 190 replacement parts that fit the 5515, from GRANIT and from brands including Scharmüller, VICTOR REINZ, LUK and HELLA.
For towing there are drawbars, drawbar frames and adapter plates, plus forced steering support plates for trailers with a steered axle. For road work there are beacons, and for the driver air suspended tractor seats. Before ordering a drawbar, measure the rail width and pin of the one already fitted so the new one sits in the existing frame.
Oil under the tractor is rarely a reason to replace a major part straight away. More often a gasket or seal has given up. For the engine you will find thermostat housing gaskets, flywheel housing seals, oil sump gaskets and crankshaft seals, and for the brakes O-rings for the master cylinder. When a crankshaft seal leaks, check the running surface on the shaft. If a groove has worn into it, a fresh seal will soon leak again.
The belt drive is covered by V-belt tensioners. When you change the belt, turn the tensioner by hand. If the bearing feels rough or the arm has play, replace it along with the belt, or the new belt will wear out quickly. There are also bushes for the balancer shafts, double clutches and individual sensors.
A beacon that has stopped turning or glows dimly often needs nothing more than a new bulb or a clean contact in its base. Check the push-on pin and the plug, since moisture in the connection is a familiar fault. If an air suspended seat no longer holds its height, the leak is usually in the air bag or one of its hoses. Listen for escaping air as you stand up, and notice whether the seat compressor keeps running for longer than it should.
The 5515 belongs to the 5015 range from John Deere. Confirm the model on the type plate, then look at the old part for a John Deere number, which is the quickest way to a matching replacement. With a seat, compare the mounting on the seat console as well.
If you also run other tractors from the same make, the John Deere parts overview gives every model its own page, so you can check each machine separately.