Q: Hi. I’m actively using my new iPhone 6 and want to delete everything from my old iPhone 5. How do I delete all of my contacts at once on the 5?
A: There are actually two separate questions here, so it’s unclear exactly what you want to do, but let’s take a look at both scenarios. If you only want to delete the Contacts from your iPhone 5, while leaving everything else intact, the easiest way to do that is through iCloud.

If you’re already using an iCloud account, simply go into your iPhone Settings app, select iCloud and then toggle “Contacts” off. You should see a prompt asking you whether you want to keep the contacts locally or remove them from your iPhone. Choose “Delete from my iPhone” and they’ll be removed from your iPhone, but left in iCloud, and on your new iPhone 6.
Similarly, if you’re syncing Contacts via iTunes, simply turn off Contact sync in iTunes and all of your contacts will be removed on the next sync.
If you’ve only stored your Contacts locally on your iPhone, however, the process is a bit trickier, as there’s really no “delete all” option in iOS for Contacts. What you can do, however, is simply turn iCloud sync ON, which will upload them all to your iCloud account. You can then turn it back OFF again, as noted above, to remove them from your iPhone. You’ll end up with your contacts still stored in iCloud, but you can merge them onto your new iPhone that way and keep them in iCloud, or log on at www.icloud.com and delete them manually from there; the web service does provide a way to select multiple contacts and erase them all in one go.