Download and Install CS5

It's a moot point.  Even if you find an old mac with old OS that supports 32-bit apps, you can't install CS5 Student version without the original media (disk or downloads) that you received at purchase.  Your student or volume licensed serial number won't work with an ordinary CS5 download.  Sorry.

Creative Suite is no longer legally sold by any vendor, retailer or country.

MODERN OPTIONS:
Photoshop Elements or Premier Elements 2021 (approx $100, no subscription needed)
https://www.adobe.com/products/photoshop-elements.html

Creative Cloud Photography Plan -- approx $10/month x 12 months. Includes the very latest versions of these great products & services:
-- Photoshop CC and Photoshop on iPad
-- Lightroom on desktop, mobile and the web
-- Lightroom Classic
-- Portfolio website + hosting
-- Spark with premium features
-- Bridge
-- 20 GB cloud storage (upgradable to 1 TB).
https://www.adobe.com/creativecloud/photography.html

Creative Cloud All Apps (31 + apps & services) and Single Apps Plans
https://www.adobe.com/creativecloud/plans.html

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Beware of fake Adobe reps who may contact you privately offering to sell you software or take control of your computer. It's a scam, run away!
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3 Easy Ways to Identify Genuine Adobe Staff
https://tinyurl.com/10791730

You mean you're trying to install it on a modern Mac? There is no chance that can work. To run antique apps you also need an antique system. However, new Macs can't run old systems. CS was replaced by Creative Cloud, subscription only, over 6 years ago.

>download the CS5 Suite to my new MacBook Pro?

No... Adobe did not maintain backward compatibility with old programs