I am posting an answer here because it appears you have been waiting for a while, and I apologize, I do not believe you are going to be happy with the situation that your girlfriend has put you in, but I have tried to lay out a brief summary of the pertinent legal issues that show how she is the culpable party and why you need to pursue her for recovery of your bank account (the bank is not liable for this transaction). I wish I had a different answer for you here, but as no other expert has answered yet, I wanted to post something so that you could move forward accordingly. I wish you the best of luck.
Unfortunately, for your girlfriend to have deposited checks into your account with your ATM card, she would have to have your PIN. Unless she stole both your card and your PIN (you never gave her either), this is going to be considered "permissive use" of the card. (This is the legal standard)
The bank is entitled to rely on the security of the ATM/PIN combination, so for the bank's purposes, you authorized your girlfriend to access your account with the ATM card and perform the transaction. (This is based on your account holder agreement / contract, with the bank).
What you can do however, is to sue your girlfriend for fraud, and conversion (the civil equivalent of theft). You will have to overcome the above legal standard (permissive use) and show that she had no authorization to perform the specific transaction (this shouldn't be too hard to do based on the fact she deposited $5,000.00 in bad checks).
Unfortunately, this isn't going to be a fast or easy resolution, and you may want to try working something out with your girlfriend short of going to court. Short of filing a lawsuit, you can try to mediate the dispute with them - contact your local bar association and request referrals to mediators, a third party neutral can often help you reach a mutually agreeable resolution. Use the bar association's referrals to contact a mediator or two, the mediator will then contact the other party to set up a mediation session, and you can go from there - hopefully resulting in a formal or written settlement agreement, and save yourself the time and expense of litigation.