The court can only consider what's on the pleadings even if they may be proven to be untrue by extrinsic evidence. So demurrer will not help you unless the complaint somehow admits that rent is due on the 5th and that you tendered the check on the same day without saying the check was returned for insufficient funds, your demurrer if one is filed will probably be denied. Some judges won't entertain the motion to quash on the same issue. Unless you are sophisticated with the law, you may not know how to argue to the judge why a motion to quash may be filed instead of a demurrer on the same issue. You should speak to an attorney. This is not a simple yes or no answer.
You are absolutely right to make a motion to quash and I bet it will be granted. If the 3 day notice acknowledges that rent has been received, you cannot be "guilty" of unlawful detainer pursuant to Code of Civil Procedure section 1161 2. Therefore, the landlord has not stated a cause of action, and you cannot be held to answer to the 5 day summons.