My dd started very basic ballet at 3 and a half, moved on to a more formal ballet school at 5 and has taken one exam a year since then: prep, primary and Grade 1. (Proud mummy moment: dd just got her Grade 1 results on Saturday - she passed with Honours )
As for swimming, we went to mother and baby lessons at 5 months where we held our babies in the water and sang songs (majorly embarrassing until you got used to it). By 2 and a half my dd could swim without armbands so joined proper lessons (normally took children from age 4) and she is now doing swimming training twice a week as a member of local swimming club, entering galas etc.