Updating to avast 5 would convert the license information from 4.8 pro, so you wouldn't need to enter the license key, and the expiry date would have been carried forward from 4.8 also.
If you have the email that you received with your license included it is possible to convert that.
- avast! 5 Pro license convert from 4.8 Pro license. Try
http://www.avast.com/resend-license.php now, fill in the form giving your email and 4.8 Pro License key and they will send the new license file to you (presumably it will check you have a legit 4.8 Pro license first).
If you can't find that, try contacting sales (at) avast (dot) com and give as much information as possible, date of purchase and email address used on purchase and they may be able to find it. I suggest you save this securely if they can find it. This would still be in the avast 4.8 license format I believe, so you may need to convert that.