No. No merchant is required to accept it.
You can exchange it for a replacement, however, there are two classes, and it appears that this falls into the second, meaning a much tougher route to getting it replaced, and the chance you will be told no.
1. A damaged note. This is a note that is CLEARLY more than one half of the note, and it is also clear what the denomination of the note is. This, you can take to a bank to exchange. The bank will be reimbursed by the government.
2. A mutilated note. This is a note that is either in such bad shape that you don't know what it is, or a readable note of which only one half or less remains. The reason for the 'greater than one half' rule is to prevent people from tearing notes in half and exchanging them separately to double their money.
So if all you have is one half, you have to go through the process of packaging it and sending to it to a special department of the Bureau of Printing and Engraving. They will examine it and research it and make a decision one way or the other, and their word is final. No is No. They record the serial numbers (wherever possible) of notes that come in, either through banks or directly to them, and if someone beat you to it with the other half, it's a definite No.
For $5, is it worth going through the hassle? You'll spend at least some money to send it in, and if you want proof they got it, it'll cost you most of that $5.