In this position I can only say: Even a moron connects against a peep.
This is a go proverb and you don't really have a choice here, but it is undeniable that the fight will be complicated for both sides.

I was recently asked this very same question in a KGS review recently. As others have said you absolutely must connect and fight. However, the key move my reviewee missed was the hane of below. If White simply extends to a this is slack and may be a bigger mistake than black's peep. The hane forces black into bad shape of the empty triangle (if he overplays with the hane of b then you cut). Note how the hane plus marked stone form the eye stealing tesuji shape.

Click Here To Show Diagram Code

[go]$$
$$--------------------
$$ . . . . . . . . . |
$$ . . . . . . . . . |
$$ . . . . . . . . . |
$$ . . . X . X . . . |
$$ . . . . . . . . . |
$$ . . . a O 2 O . . |
$$ . . . 4 3 1 . . . |
$$ . . . b 5 . X . . |
$$ . . . . . W c . . |
$$ . . . . . , . . . |
$$ . . . . . . . . . |[/go]

Edit: in fact in the review I mentioned black had pushed along the third line from c three times as in the joseki and then played the peep and pushed out. In your case white could also consider blocking at c instead of the hane as this makes black's shape awful and threatens to connect. But the point remains the hane is the strong move in the centre and extend is slack.