Create PDF of A5 pages for printing A4 Landscape Booklet

Let's change your workflow a bit. You have a Postscript Printer (your HP), so that's good. you can use that printer's driver (and its PPD) to generate the PS. (If you didn't have a Postcript, it's a good idea to download the PPD for Acrobat (Adobe PDF 9.0) and use that. You can find a link for a downooad of that and instruction to install in this forum in older posts. The important thing is that the PPD you choose needs to have the capability of the paper size you want. For instance, you couldn't use the PPD for an A4 printer to define a larger A3 page. The Adobe PDF 9.0 allows you to define these larger/custom paper.

So, in InDesign, create a print setup (File Print Setup > Define) and create one for your A4 size, like so:

Select Postscript File, then any possible PPDs will now be listed. Choose your HP PS printer. Also, make sure to select a landscape orientation as appropriate. (If you had the Adobe PDF 9.0, you would select that PPD instead).

NOW, print your Booklet, selecting the Print Preset you just defined, and make your PS file. Distill that and you should be good! The only issue your end user will have to deal with is defining how to print the double-sided, as it will require selecting short edge binding to keep the pages the right direction.

You could create PDF from your PS file with booklet'ed pages - but then not every printer have automatic duplex option - so if Elderly user would have to perform "manual duplexing" - they would have to be quite advanced users...

In most modern Laser printers, toner cartridge is located above the path of the paper - so if you use tray for "manual duplex" - you would need to put already printed side "face up" - paper will most likely do "S" path and printed side is almost always "face down".

But if user would use side/manual tray - located at the front - printed side would have to be "face down" - paper will do "C" path.

If manual tray is located at the back - still "S" path but more flat than from the tray - paper would have to be loaded "face up".

With InkJet printers - printed side would have to be ALWAYS up - as in InkJet printers, paper is always doing "C" path..

Then there is a case of what is the max size printer can print - if it can handle A3 - then user will most likely have at least two trays - one for Portrait and another for Landscape A4 loaded paper... or one will be for A3 paper and 2nd for A4 paper - Landscape or Portrait... and when A4 sheet will exit A3 printer - it is important to rotate it correctly - or you'll have front and back upside down...

So it's rather a lot of hassle and it's better to just prepare it as a single page PDF - as already suggested...

Consider using the InDesign Publish Online facility (as single pages, so it can be read on any device – computer, tablet or smart phone) with the document enabled for users to print out a PDF version if they wish.

With this you only need to distribute a URL with a nice cover screen shot, and leave it to users how they want to access the document i.e view it online and / or print it out.

While a properly set up PDF should print consistently for all users — that is its basic concept, after all — I think it might be overreaching to assume any document will print precisely for some large number of amateur/unskilled users on the variety of printers such a population is likely to have.

I would "design for failure" here and make sure that the project is usable/readable/acceptable pretty much no matter how it prints out.

Export to PDF as single pages. 
Let them print it out whatever way they want it.

Acrobat allows you to pick a booklet mode. 

And most printers nowadays have a print booklet.

But what's the harm if they print it as single pages? 

You're making a lot of assumptions that all printers would have same capabilities, and/or that the end user knows how to correctly set the settings.