Fedora doesn't have a DVD-based upgrade process; updates are started using
dnf system-upgrade. We * test updates from the previous release and the release before that — so, from F23 or F24 to F25, but not from F20 to F25 directly.
Since you have data backed up, and the DVD in-hand, the easiest way may just be to do a fresh install of F25 and then put your information back. (I usually make
/home a separate partition, to make this easier when I decide to do it.)
We do have some suggestions for upgrading from old releases — see Upgrading from End of Life releases on the Fedora wiki. The basic advice is to upgrade with
yum to at least Fedora 21, and then
dnf system-upgrade from there. You may have better results doing yum/dnf based upgrades all the way to F23 before doing
dnf system-upgrade — or even going all the way to F25 that way.
The good news here is that we've worked to make
dnf system-upgrade as painless as possible (often taking less than half an hour), so when your upgraded F25 system gets to end of life, going to F27 should be a piece of cake.
* I work on Fedora