EDIT: The OP actually is most interested in whether the 5400 series processors can be used in the xw8400, not really in what other processors in the 5300 series of processors will work. The answer is no, the 5400 series processors is for the next generation of HP workstations..... the xw6600 and the xw8600. A BIOS update can't change that.
Welcome..... For your project a great source is the search box that targets this forum only, at the top left. There was an earlier HP forum that I posted a bunch of info on the xw8400 that still can be found, however, via google searches for specific items. Below are budget suggestions.
The source for the list of officially approved processors is best found in the latest version of the QuickSpecs for a HP workstation, and the latest one I have is Version 28 from 2/22/08. These workstations still have the potential for excellent performance even now with processor upgrades and adding more memory. You want two of the fastest quad cores.... they are E5345, X5355 or X5365 and those run at 2.33, 2.66 and 3.0 GHz respectively. They draw max wattage of 80, 120, and 150 watts, respectively. You want the latest version of those, each of which had 2 or 3 steppings, and you thus you want to search eBay for the sSpec code of SLAEJ, SLAEG, or SLAED respectively.
The heatsinks for the xw6400 or xw8400 were the same but the xw6600 or xw8600 will fit too. You already have two heatsinks, and I hope they are the 3-heat tube versions, discussed below. The xw8600 came out with a special "performance" double tall double fan heatsink for the hot processors, and one of my iterations of the xw8400 had one single tall and one double tall over the X5355 processors.... little difference in temperatures for how I use a workstation.
You likely will be very happy with two of the E5345 SLAEJ under your current heatsinks/fans. Those heatsinks came in 3 versions: 398293-001, -002, or -003. You do not want the -003 version because it is short one heat tube, probably cheaper to make and used by HP for the 80 watt processors only. Thus, the -002 and -003 have more cooling capacity.
I ran my xw8400 with the E5345 SLAEJ and the X5355 SLAEG. I posted previously on how to spoof the motherboard into thinking it had a "performance" fan and thus not boost up the fan rpms for the X5355 but my advice is to start with 2 E5345 SLAEJ processors for you.
Memory.... best to populate all memory slots with identical RAM sticks, HP holographic label ones, and ideally from the same vendor such as Elpida or Nanya (my favorites for that era, but Samsung is close behind as is Hynix. Not Micron for the 4GB sticks.) Look for HP part number 398708-061 for 4GB sticks. For 2GB HP sticks look for the same brands but Micron 2GB are OK. Look under 398707-051 (or -551). Careful shopping for used HP sticker RAM on eBay is worth doing.
OS and drivers: I use the MS "system builder" W7Pro64-bit install. I always load the latest BIOS first. I only build now with non-RAID single 300GB SSD (I only use Intel 320 series 300GB now, with 2TB or less documents drive also in place. Make sure to set BIOS SATA Emulation to RAID + AHCI before install, even if you'll never use RAID. Any of my posts on xw6400 BIOS optimization will generally be good for the xw8400.
Finally, rarely the optical drive in place is too old to run the installer DVD so you might want to buy a newer HP one and swap it in. Newer HP universal installers from the Z600 or even the Z620 era will work fine on the chipsets on the motherboard (for Broadcom, Realtek, etc.). There is a "best" ESB2 driver I have posted on also.
From the W7 Windows Experience Index scoring system you can expect:
Single X5355 gets you 7.3 (out of 7.9 max) but 2 X5355 gets you 7.6 for both your memory and processor scores. You can see that loading the second processor is worth it, and you get a similar benefit for those below too.
Two X5365 will get you 7.7 for both of those.
Two E5345 will get you 7.5 for both of those.
A HDD will get you about 5.9 for drive score, but SSD will get you about 7.7-7.8. So, well worth it.
Video cards.... for budget card I like the used eBay FX3700 a lot, which will get you 6.8 for 2D and 3D video scores. There is a HP firmware updater you can download, and it will update non-HP FX3700 cards too. You can buy up from there if you don't want Quadro hardware. For example, a nVidia GTX 650 Ti Boost on my xw8400 registered 7.9. The pic below shows that.... this build got one of those Intel SSDs next:
