ダウンロード版のイラストーレータがダウンロード

macOS SIerraはCS5の動作対象外です。

そのため、正常にインストールおよび動作しない可能性があります。

最低でも、Johnさんが回答された様々な対策を行なう必要がありますが、それでもインストールできたり、正常に動作する保証はありません。

また、CS5には「ダウンロード版」は無かったと記憶しています。

Adobe社では既に販売を終了していますので、最近（ここ数年）「ダウンロード版として」購入されたものであれば違法コピーの可能性があります。

CS6 and earlier programs have not been tested and will not be updated for Mac El Capitan/Sierra

-which means that you try to use CS6 and earlier at YOUR risk of having problems

-you may get CS6 and earlier programs to install and run, or you may not (some do, some don't)

-Java https://helpx.adobe.com/dreamweaver/kb/dreamweaver-java-se-6-runtime.html may help

-https://helpx.adobe.com/creative-cloud/kb/install-creative-suite-mac-os-sierra.html

Install CS5 on Mac 10.11 https://forums.adobe.com/thread/2003455 may help (also for other than CS5)

-also a TEMPORARY security change https://forums.adobe.com/thread/2039319

-Gatekeeper change does NOT work with Sierra https://forums.adobe.com/thread/2212384

Owners of old programs simply have problems with Mac El Capitan/Sierra... none of which is Adobe's fault... Adobe did not change your old program to make it stop working... Apple changed their operating system and THAT is why your old programs won't work, not because of anything Adobe did... Also... every time Apple issues an update, there is the risk that an old program that HAS been working will STOP working... bottom line, old programs require a matching old operating system