Fresh Android 5.1 phone, just installed Dropbox app from Android Play Store. Started the app, tried to log in for the first time, got a message: "Too many attempts. Please try later"
Dropbox works OK on my other devices, including my previous Android phone.
I did some googling, and it seems that other people did face the same problem recently:
Dropbox Community Forum thread, a comments suggest that retrying after several hours may solve the problem. This workaround didn't help in my case (yet).