Ouch. Why is it that people who ask this question always seem to have the most difficult printer models to get working 🙂
The primary issue is the fact that the MacOS driver for this printer supplied by HP will not support network printing via a print server. That means you need to use a third-party printer driver for the OfficeJet 5510 that does support network printing - like GimpPrint or HPIJS (referred to in the web article I referenced above).
To keep things simple, I suggest you follow iFelix's web site instructions, but rather than installing either HPIJS or GimpPrint, use the GimpPrint driver for a DeskJet 900 series printer - that driver is already built in to MacOS 10.4. You will only get 600dpi color printing with that driver - but at least it's a start. If you can get that working, you can move on to downloading and installing Ghostscript and the HPIJS driver for an OfficeJet 5500 (which might produce a better quality printout).