Q: How can I open control centre on my ipad mini?  Have tried swiping from the bottom.  Nothing happens.  Thnx

If you have iOS 5 as your tagline suggests then you can't - Control Centre was introduced with iOS 7 (your current iOS version is shown in Settings > General > About > Version).

If you do have iOS 7 then you are swiping/dragging up from the very bottom of the iPad's screen ? Settings > Control Centre allows you to disable it if you are in an app, so it might only work from the iPad's homescreen.

No, Control Centre is on iOS 7+ - you can update the iPad to 7.1.1 via Settings > General > Software Update : http://support.apple.com/kb/HT4623

If you want to use AirDrop to copy the photos then both iPads will need to be on iOS 7 : http://support.apple.com/kb/HT5887

Or you could use your computer to copy them. If the photos were taken with the iPad then you could copy them to your computer : http://support.apple.com/kb/HT4083 (which you should probably do anyway so that you have a backup copy)

and then sync them to the other iPad : http://support.apple.com/kb/HT4236

Or you might be able to use Photo Stream to copy them - I think that only 30 days worth of photos are stored in Photo Stream (I don't use it so I'm not 100% sure)

Photo Stream FAQ : http://support.apple.com/kb/HT4486

If i remember correctly on IOS 6 you can double click the home button and swipe the dock to the right for the earlier version of Control Center. It wasn't called Control Center back then.

Airdrop was new to IOS 7. There are many easier ways to transfer photo then Airdrop. King Penguin already listed many of them.