This is a little tricky, as they gave you the amount you requested. You most likely low-balled yourself, and they jumped to offer you a lower figure than they were expecting to pay out.
Now here's the deal: a company will always seek to pay as little as possible for an employee - it's just good business.
You've already made a big mistake by showing your hand. They know what you were "hoping for", and have offered it to you. When you go back to the negotiating table to ask for more they'll probably be thinking this:
Ethical Kid got what he wanted, and now he's trying to shake us up for more. Just refuse him, you know he's gonna take it anyway.
In the future always ask for more than you're expecting to receive, that way you'll be able to compromise on a lower figure without actually accepting less than you'd like.
Back to your current predicament, I'm sorry to say your chances aren't good.
There's two approaches you can take:
1. Be aggressive
If they really want you, you have a much higher chance of getting what you want by being prepared to walk away, and showing it. Here's what you'd write back:
I was very happy to receive your offer. Unfortunately, however, I cannot accept it as it currently stands. I feel that based on the market average, as well as my own qualifications a salary of at least 90K would be more than fair.
Now keep in mind .. this is written off the top of my head. You'll want to refine it and get it to feel both like you're ready to walk away, but also not overly pushy.
2. Be polite and hope for the best
If you really want the job regardless of that extra 5K then you want to be polite about requesting more money, because you're not willing to walk away.
Thank you very much for your offer. I was very glad to receive it, however, I would like to inquire as to whether you would be willing to increase the salary to 90K. I look forward to your reply.
The worst thing that can happen is that they refuse, at which point you have to decide whether to take it or leave it.