The low points of the system to me (for lag free multiboxing, except in Dalaran) are: video card, system RAM, hard disks, processor.

honestly though, I 5boxed on a system that was worse than that and it was playable for me. I had a dual core 2ghz machine with 3.5GB of usable RAM (win xp) and a 256MB video card.

Can your processor 5 box? yes as long as you can assign clients to a certain core
can the video card 5 box? yes but probably only on low resolutions with little or no graphic settings and limited "view distance"
can the hard drives? yes but a cheap SSD would really help out (at least 32GB but 64 or larger would be better)
can your RAM handle it? yes but it's going to be rough as it will probably have to write to the page file which will slow things down.

your upgrade path is all determined by your budget. I would spend money on a video card first and RAM (provided you can use a 64bit operating system to take advantage of "more than 4GB) then an SSD and cpu.

just my 2 cents