Basic users have a three device limit as of March 2019.

Plus and Professional users can link unlimited devices.

Business users can link unlimited devices, but Advanced and Enterprise Dropbox Business admins can limit the number of devices that their teams can link.

Learn more about linked devices.
What do I do if my device limit is reached?

If you’ve reached your device limit, you can change which three devices are linked to your account. To do so, unlink devices you don’t want on your account (down to less than three), and then link the devices that you do want. Learn how to link and unlink devices.

If you're a Basic user and you linked more than three devices prior to March 2019, all of your previously linked devices will remain linked, but you can’t link additional devices.
To get unlimited linked devices, upgrade your Dropbox account.