I would recommend a 3-step process personally to ensure the best possible outcome.
First - backup your site (I LOVE Akeeba Backups 1-touch backup solution); download the backed up site and install on a local host or development server.
Second, do your upgrade there (extract the files from the .zip and put them in the localhost/dev server installation).
Make sure that the upgrade didn't break anything, that everything still works appropriately and as expected and create a backup of the localhost/dev server site.
At that point you know the upgrade won't break anything.
Third, upload the unzipped files from version 1.5.23 via FTP into your root joomla directory (complete the upgrade as listed HERE.
Doing these steps will ensure the best possible outcome and will show absolutely ZERO disruptions on your live site in the event something you're currently using doesn't like the jump from .15 to .23 - which is a large jump and a lot of things are different (including which version of mootools is included!) So take caution and TEST FIRST!
与恶龙缠斗过久,自身亦成为恶龙;凝视深渊过久,深渊将回以凝视…