iPhone 5 moving of contacts
When you remove an account from the iPhone (or any iDevice), it will ask if you want to "remove or keep" the current contacts etc.. synced with the accounts.

First delete the account from your device i.e.

1) Tap on Settings
2) Tap on Mail, Contacts &amp; Calendars
3) Tap on the Account in question
4) Scroll to the bottom and tap on "Delete"

You'll then be asked if you want to keep or delete the contacts, calendar entries and/or mail on your device.

Once you've done this, the synced contacts should be on the device still (confirm this first), and then voila.. you can close your Exchange Account.