You pose an interesting question.
Even though you won't be running an SLI video card setup, I think that both video cards would need to "share" the same Nvidia drivers and software. I don't know how many monitors an FX5500 PCI card can drive and what screen resolutions it could support in a multi-monitor setup. My best guess is that you could run a 3 or 4 monitor setup using 2 PCI video cards where you would expand your desktop across all monitors.
I still have several PCI FX video cards, but I don't have 3 or 4 monitors to test with. I think that my FX video cards are one or two steps lower than an FX5500 video card. My P35-DS4 and P35-DS3L systems "share" my 1920 x 1080 monitor and each system easily handled this monitor with my ancient 7600GT video cards.
As I recall, my 7600GT could power my 21" Apple Studio Display monitor and a 17" CRT monitor at the same time, but I wasn't doing any heavy multi-tasking. FWIW, according to Graphics Card Performance Hierarchy Chart - Best Graphics Cards For The Money: January 2014, my 7600GT is 8 levels higher than an FX5500 and your 9800 GT is 8 levels higher than my 7600 GT. Your 9800 GT is 13 levels lower than GTX 690 and Radeon HD 7990 video cards.