An HD5870 uses SLIGHTLY LESS than the bandwidth afforded by PCIe x8 v2.
If you had 8x or 16x for that slot the performance would be identical. For the exact details on how your motherboard distributes bandwidth see your motherboard manual. It's probably something like you can 16x off of a single slot UNLESS you put a card on the second main PCIe slot (any card).
I'm not sure exactly how close the HD5870 comes; I believe it's somewhere between 80% and 95% the bandwidth of PCIe v2 8x.
FYI, you can TEST this by running a Futurmark (3DMARK) benchmark with the second major PCIe slot populated and unpopulated.
It's also important to look at your BIOS settings which probably have a couple options for how to assign bandwidth to these slots (including AUTO).