In reference to the patent: US5809590
It appears as though this patent is expired, and I wish to re-patent a similar product. How do I go about doing this?
That's, unfortunately, illegal.
From that link,
The public should . . . be able to act on the assumption that upon the expiration of the patent it will be free to use not only the invention claimed in the patent but also modifications or variants which would have been obvious to those of ordinary skill in the art at the time the invention was made, taking into account the skill in the art and prior art other than the invention claimed in the issued patent.
You can't try to extend the term of a patent.
What it comes down to, then, is "similar."
How similar are we talking? You're certainly permitted to patent improvements on existing products, as long as you don't try to claim something that's already been around for a while, or that would be "obvious to one skilled in the art."
It's probably best to speak with a patent professional (attorney or agent) to review your specific invention in comparison to what is claimed by the expired patent. You might be able to protect the difference of the two, which would give you control over others attempting to use your innovations, but it wouldn't give you control over anyone trying to use the invention as stated in the original, now-expired, document.
A similar product does not sound as if it was the same subject-matter. You are in a comfortable situation, because you seem to have the closest prior art at hand (important for your application) and you may produce it since the patent has expired. You simply need one or several improvements that you can show your produnct has over this prior art. These improvements however need to be non-obvious considering other prior art. In principle it is always best to check this with a patent attorney knowing the patent law and procedures for the country or countries where you would like to protect your invention. Good luck!