The motherboard actually has a Parallel Port Header, as many of the HP workstations and desktop business HP PCs do, and those are 25 pins with one key blank (aka a 13 x 2 header). HP has sold both full height and low profile adapters for this header... the headers are all the same. For the dc5800 that motherboard header designator is P126:
Here is a better picture:
Your eBay source is HERE:
HP Parallel LPT Port Low Profile SFF LP 462537-001 462537-002 Adapter
Here is the image:
Not bad for a HP-made low profile adapter at under $6.00 USD including shipping. I have used these, and they take up one space on your PCI backplane. Nice thing is that the motherboard header and the OS drivers are already present..... pretty much plug and play. No software install needed.