I don't know if this an answer others might like, please use the following changes with care.
As you see by the answer of skytux, Dropbox's repository does not support Fedora 23 as of right now. You can modify the corresponding repo-file in /etc/yum.repos.d/dropbox.repo
(maybe the filename is different, I don't know) and change as root the line from
baseurl=http://linux.dropbox.com/fedora/$releasever/
to
baseurl=http://linux.dropbox.com/fedora/22/
With this, you are using the version of Dropbox that is made for Fedora 22, so some bugs might appear. For the future, you can look at the link http://linux.dropbox.com/fedora/23/ if it is available, and change the file you modified back to what it was: replacing 22 with $releasever (or 23, so you don't have the same problem after upgrading to 24 in the future).