Threefold repetition is not a mandatory draw, it must be claimed. A correct claim by a player will let the draw be declared.
Fivefold repetition is new rule that FIDE recently instituted (I believe less than a year ago) and is not implemented on this site. Since this site more closely follows USCF rules than FIDE, it may not be implemented in the future, though you'd probably have to ask the staff to know for sure whether or not that is in the works.
I just found something very dissapointing. I was playing a game and the position was not repeated 3 times, according to the rule, but 5 times! A draw should have been declared automatically by chess.com just like other chess servers do, however it wasnt. My opponent finally made another move and we continued playing.
I think this is something extremely important the should be corrected because not all players accept a mandatory draw like in this case.
PLease do something about it.
Thanl you.