If you allready have purchased GT5 DLC content, they should be: Sign In -> Account Management ->Transaction Management -> Download List
I own GT5 on my PS3, and allready purchased DLCs working just fine. (at least those purchased before 30 Aptil 2014)
If you don't have purchased any GT5 DLCs yet:
After 30 April 2014, players will be unable to purchase any Gran Turismo 5 DLC, as it will disappear from the PS store forever. !!!
Specifically, Sony says that the following services will come to an end: Online Lobby, Seasonal Events, Museum, News, Community, Remote Race, Log in Bonus, Online Dealership and DLC purchase.
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You wanna definitely purchase GT6, as it has much more challenges as the previous GT5 game. !!! (Even Moon exploration challenges...what ??? - YES IT HAS.) lol
I don't wanna spoil anymore...