I can play 3 lands, right? And if I were to cast Summer Bloom, I'd be able to play 6 lands that turn, yes?
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I can't say I'm pleased to see you and must warn you I may have to do something about it.
EDH: UGEdric
Pauper: URDelver
Modern: UGRDelver
Draft my cube: Eric's 390 Unpowered
Each effect that lets you play "additional" lands is cumulative. Therefore, with the presence of all three effects you mention, you can play up to five additional lands that turn (assuming it's your turn) (C.R. 305.2; see also C.R. 305.2a).
I also have Exploration on the field.
I can play 3 lands, right? And if I were to cast Summer Bloom, I'd be able to play 6 lands that turn, yes?
EDH: UGEdric
Pauper: UR Delver
Modern: UGR Delver
Draft my cube: Eric's 390 Unpowered
EDIT (May 14, 2018): Correctness edit