I have had InDesign CS5 on my older HP laptop for several years. I had to upgrade, so I installed the same CS5 (from the DVD) on my new Asus. Now more than half the fonts that were available are gone. No Edwardian script or many other popular ones. Where do i get them, and how to i install them? I can't pay $55 per font!
The fonts are found in the location Windows places fonts (you can see the path in Type > Find Font > More Info).
Those fonts need to be copied from your old HP laptop and installed on your new Asus.
Windows users here can tell you how to install them. (I work on a couple Macs.)
To expand on Steve's response, InDesign and other Adobe software installs relatively few fonts on your system and certainly never uninstalls others. Fonts such as Edwardian Script are not Adobe fonts and were not installed by any Adobe software although if installed by the OS, other applications, or manually, they are available to Adobe applications in general and InDesign in particular.
Hopefully, your old laptap computer or a backup of the disk of that system are available to you to retrieve the fonts you are looking for. Backup of your systems and your digital assets is critical!