Good card and it'll fit.  You'll see the PCIe slots when you open up your system.  I'm also attaching the 7010 Tech Guide, which has 7010 motherboard layouts.
Specs:  Dell Optiplex 7010 Mini-Tower, Quad Core i7 3770 (3.4GHz), 16GB DDR3 SDRAM, 1TB Hard Drive: Windows 7 Pro 64-bit. A mobile rack (Syba SY-MRA55006) has been installed in the spare 5.25 bay. I'm wanting to see if I can do anything to get this hooked into a surround sound speaker system. I heard on other forums there are low-profile sound cards that might fit, assuming this PC model has any spare PCIe slot for it, and another told me there are external USB sound cards that might work. Any ideas?
Can an OptiPlex 7010 MT be adapted to use 5.1 surround sound speaker system?