Welcome to the forum. Please add your location to your profile, it adds context to your posts and will help others give you better answers to your questions.
The engine # is on a boss on the back of the engine casing, where it points toward the rear wheel. You're looking for a machine embossed number, not one cast into the block. This is not the same as the VIN, but may provide you with some information. FJR1300 engines haven't really changed much over the years. Trans changes did occur, which certainly may impact your project.
If that number is your engine number, which looks likely, the P505E is the engine code and the 000554 is the serial number.
Decoder LINK
P504E was from 2001 FJRs. 2003 was the first model year available in the USA. Are you in the EU? If so, you may have a 2002 engine.
2004/05 FJR1300 engine codes are RP041 and FJR1300A is RP115
2006 engine codes are RP042 / RP132 AS is RP135
2007
FJR 1300 | RP042 / RP13A |
FJR 1300 A | RP132 |
FJR 1300 AS | RP135 |
2008
FJR 1300 | RP042 / RP13A |
FJR 1300 A | RP133A |
FJR 1300 AS | RP13E |
Yamaha Dealer should be able to give you more info on what year it is or what generation it's from.