Adobe Illustrator CS5 (released in 2010) was designed as a standard installed application. Any "portable" version found online is an created by third parties.
If you are using a modern Mac (macOS Catalina or later), . Illustrator CS 5.0 supported in Mac Os Big Sur? | Community
Unofficial portable apps are often "cracked" versions that can contain malware, trojans, or spyware designed to steal data or passwords.
These versions frequently bypass standard security protocols, leading to system crashes and bugs on modern macOS. Compatibility Challenges (macOS 10.15 and Newer)