What can I do?
You're going to have to make some hard choices. The easiest solution would be to get a cheap Windows 10 laptop, because old versions of Dreamweaver will likely be good for at least a decade. If you can't, or won't, do that, you can revert back to a previous version of OS 10. Barring that, you can buy a subscription to the Creative Cloud.
Just to add to Nancy's advice...
The Adobe workarounds are typically a bit incomplete. You might also need to make some system changes on your Mac, including the Java implementation. You might also want to read this:
In my experience, Adobe tutorials are usually the last ones you want to read
Read through this article, particularly the section for "Older versions of Adobe software (CS3–CS6)" + the comments section. Seems some users have CS5 apps running under High Sierra, however it seems the success various some.
Worse case you can revert your OS back to a previous version you had CS5 working successfully on, or a partition to do so.
I'm running Dreamweaver CC 2018 on High Sierra and it continually shuts down. In the last four hours I've got about 10 mins work done.
I have a brand new CC (today), and all programs open, but not Dreamweaver CC (and not Dreamweaver CC (2017)!
To all of you that are on Dreamweaver CC 2018 and are facing issues, please send me your Adobe ID, location, and phone number over a private message. We will get in touch with you for investigation. To send a private message, click my picture and use the Message button.
Same here, I've had the same problem for months.