The card measures 10.5” long, an inch longer than the 4890 or the same as the 4870x2 and the NVIDIA GTX lineup.
Below is the specification for PCIE card dimensionhttp://www.interfacebus.com/PCIe_Card_Dimensions.html
With the budget for 5870 why not get a bigger case like 900 or Antec 902? For sure it will fit. The cooling for 900/902 will be more than sufficient for the 5870.
Its your choice...Antec specs for 300 states "nvidia 8800". There is no adjustment on the card-cage assembly. The Antec 900, 902, 1200 can accomodate the card. The HD-cage are adjustable.