I don't love 4.. c5 although it seems that after 5. Bg5 Be7 6. Bxe7 Nxe7 you should have a playable position.
I would consider the more sober 4.. Nf6.
Black down a pawn in the Tarrasch Defence?
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Perhaps Qb6, Ne7, Be7 prevent the loss of a pawn.
In your line 5...Nf6 6 Bxf6 Qxf6 7 dxc5, black can play ...Qxb2.
I recall that white gets strong pressure on d5 in the tarrasch, but apparently it can't be immediately won, at least without consequences. Black can play ...cxd4 at some point instead of waiting for dxc5 if he wants. That forces something to commit on d4. If it's a knight, although d4 is a good square it's not clear if white wants his knight away from the kingside just yet, and if a queen comes there obviously ...Nc6 is useful.
I never liked black's game in this defense (it just doesn't have the fire of a white IQP position), but although white can get the advantage, if black plays dynamically enough I think he can still be ok. He'll want to avoid too many exchanges and put enough pressure on white to make it too hard for him to make progress, and against any white mistake take over the initiative with an attack (but I do think white needs to go somewhat wrong to allow this).
I've been practising the Tarrasch as black against the computer and this one has been bugging me:
where balck can play 5...Nf6, but after 6Bxf6 ...Qxf6 7dxc, black's D pawn becomes impossible to defend (its inevitably lost after ...Qd8 8 Nc3). Is this a trap that black has fallen into where the move c5 was innapropriate? or is the loss of the pawn worthwhile for the removal of White's dark squared bishop? as a beginner, I'm not the best at evaluating the value of peices in the opening- I'm sure as in the Queen's accepted it is viable to be down a pawn in the opening for some positional advantage.
Note that the same position arises from 5...Be7, where black's dark squared bishop is also removed. I'm almost tempted to try 5...f6?! (where the bishop and the knight disagree, but it looks better after Bb4+) where after the bishop retreat cxd. Have I missed anything? I suppose the real question is, is this an opening completely seperate from the Tarrasch?