I send my 5130 to Master Time in Singapore, via Patek boutique @KLCC for basic lub service few years ago, cost abt 5k+.
Is yours AC ..... 5056? As with other 5056, I find that its accuracy isn't that great. Mine is due for its service soon. Pls post us the cost if you send it to Geneve, via local boutique. As its a complication model, I won't advise to do it at anywhere else. Cost shld be in the region of >10k nowsaday.