I would like to download my old downloads (purchased photo's)

I suppose also you talk about Adobe stock. Go to stock.adobe.com. Login to the account where you made the purchaes. Click your avatar, and navigate to the license history and download one by one your files. Proceed as @John T Smith suggests. Keep also a copy of the licensing terms as you may need that at a later stage. Keep a list of the pictures you licensed, as if contested, that may come handy. 

Nb: Some assets may not be available snymore, if the assets have been removed from the servers. There is no way for recovering those assets, therefore you absolutly need to keep your back-up (see @John T Smith https://community.adobe.com/t5/download-install/i-would-like-to-download-my-old-downloads-purchased-photo-s/m-p/12183370#M537476).

>like to download them again

When you download something, be that a picture or a program, you should always copy to at least one external drive

I use a Sata docking station and several 'bare' drives for backup
https://www.amazon.com/StarTech-com-External-docking-station-drives/dp/B00U8KSLA8/

Hi Harriët,

Are you referring to the Adobe Stock service, or something else?

Just want to make sure we answer the right question or direct your query to the proper place. Thanks!