I own a Dell Precision 5810 E5-1620 (six core xeon processor). I had a MSI GTX 970 4G Gaming card in it and it was great. A GTX 970 would be an excellent upgrade for this computer. The PCIe slots in the T5550 are generation 2.0, and the new cards are 3.0 but that's actually not an issue, as Gen 3 cards are one generation backward compatible.
* What to look out for: Check the inside of the T5500 and see how many 6 and 8 pin connectors are available. Since that computer was configurable with upto a Quadro FX 5800, I assume the computer has both a single 6 and single 8 pin PCIe connector. Although the MSI GTX 970 has one 6 and one 8 pin connectors on it, you can get away with two 6 pin connectors, and simply use the 6-to-8 pin adapter that's included with teh MSI card. Let me know what you think. By the way, the T5500 is a beast of a computer.