Is that really an independent opening? Is it really a sicilian?
The position after 4. e5 can also be reached from an advance french, when you have a gambit with 4. ... cxd4 5. Bd3 Nc6 7. a3.
If you add some more moves it is likely that even in the line after exd5 you might transpose to a regular french. In case of white's Nf3 on g1 and the other one having moved already to d2 it is a french Tarrasch position.
To me this looks like some special move order.
By the way if you look into the chess.com online database after 5. Bb5+ Bd7 black scored 50%, however there have been only 15 games, and after 4. e5 score is 50% too.
Anyway, why do you spend so much effort on openings?
I was trained in the English opening and the Sicilian Dragon. I soon moved over to the othe Bishop pawn and learned the Bird and the dutch. As for my defense I still play the Dragon. Recently; however, I stumbled upon Mashall's counter attack and loved the quasi gambit looking position.
The main line doesnt seem to favour Black.
4. exd...
I would like to think this isnt so bad but it isnt usually. The top 3 lines following Bb5+ all put Black at <30% winning. Lucky for me most players i encounter play 4. e5 rather than taking d5. To my glee 4. e5 rusults in >60% win rate for black.
I dont know the history of this defence, so what is its history? Why would anyone not play 4. exd besides lack of knowlede. White gains a lot of centre control and has the greatest advantage even without prior knowledge. Please halp :P