recents not updating on my new iphone 5

Not sure why that would be, however, you can try a restart of the phone (power off/on) and if necessary a reset (hold the sleep/wake and home buttons together until you see the Apple logo and then release). See if after that all is well.

Are you referring to the fact that when you activated the new phone you restored from a backup of the old one? While that could have something to do with it, the iPhone 4 had the ability to store recent calls as well as edit the recent call screen.

However, if performing a restart and a restore did not correct the issue, then the next user troubleshooting step is a restore, first from a backup and if needed, as a new device. Try that and see what happens.

From the action you are describing, there could be something wrong with the backup, however the first try you are going to do is from a backup. You also need to make sure that you are importing photos from the camera roll and are syncing contacts and calendar to the supported application on the computer and/or iCloud so they are saved and ready to restore. If, however, after doing a restore from a backup it does not work, then you will have to restore as new. That will delete everything and you will have to resync all of your data. You will lose games saves and SMS. Your call.