Forgot My Boyfriend's Birthday

I have been dating my boyfriend for 5 months. At the moment, we are in a long distance relationship because I am visiting family. So we are talking as much as we can on a daily basis to compensate for what we are lacking and missing. I am so upset with myself that I don't recall the entirety of our conversation. However the mistake of mine is when he asks me when his birthday is. I so confidently answer the wrong date which makes him feel so disappointed that he hangs up on me. I call him back and apologize profusely. He is so hurt which he has every right to be. He then tells me that I was one day off from the date that I mentioned. Even though it's reasonable for him to feel the way that he does, I thought I was incredibly incorrect. He mentions how we've been constantly together since we started dating, always talking, very close, spending plenty of time together and how he's shocked by my memory. Regardless I feel like the worst person in the world. Especially because he has been already mentioning how he wants to take me on a trip for my birthday when it is over two months away from now. What should I do to makeup for this horrible mistake? It's tricky because we are long distance at the moment. So what could I possibly do to prove that I'm genuinely sorry and that I care to know all I can about him?