Oh, you can. You can’t crossfire them together but you can use them both individually in your system.
As the cards are both new series cares (7xxx) you’ll have no problems what so ever using them in the same system without installing any other drivers.
5xxx, 6xxx, 7xxx cards can be used simultaneously in the same system using one of the newer ATI catalysts, I believe from around 12.8 onwards 7xxx cards were supported.
Where you will encounter issues is when you want to use a ‘legacy’ card in your system at the same time as a newer card. 4xxx cards and below are now known as ‘legacy’ and require their own drivers. Which, in turn, is known to cause conflict with the newer drivers.