Can't download CS5 on a new imac.

If its a new Mac, its probably running Mojave, which means a lot of older software isn't going to be compatible with it.  You might need to take the leap and get CC.  At least with that, you'd always have the newest version at your disposal

Your new iMac comes with MacOS 10.14.4 which will not allow Install.app to be directly run. You have to use Terminal.

Installing Creative Suite on macOS 10.12 (Sierra) gives you directions to do this.

Also you may need to install Legacy Java Download Java for OS X 2017-001

Then finally allow CS5 to control your computer. https://www.macworld.co.uk/how-to/mac-software/open-apps-wont-work-mojave-photoshop-3684425/

And one more thing: The CS5 when installed is at 12.0  use this link to update it to 12.0.5 download.adobe.com/pub/adobe/photoshop/mac/AdobePhotoshop12-5-mul-AdobeUpdate.dmg

It fixes a lot of bugs. https://www.reddit.com/r/MacOS/comments/9il9je/mojave_and_photoshop_cs5/

Trying to get old software to run on new OS's is always a challenge.

You could try this suggestion from vitomar

in the Security & Privacy settings in System Preferences go in the Accessibility tab and check Adobe Photoshop CS5  “Allow the apps below to control your computer”

Full thread here. Photoshop CS5 on MacOS Mojave

CS5 is 8 years old and is not supported to run under Mojave. You need to upgrade to InDesign CC.

Hi

Take a look here to see if it helps

Installing Creative Suite on macOS 10.12 (Sierra)

If you have Mojave OS you may also want to check this out

https://www.macworld.co.uk/how-to/mac-software/open-apps-wont-work-mojave-photoshop-3684425/