Five year support might be too short for some people. If so there's Red Hat Enterprise Linux (and its community rebuilds like CentOS), and SUSE Enterprise Linux.
A paid RHEL subscription will even give you security updates for point releases, in case your needs preclude from upgrading even to backwards compatible versions (e.g. You can use RHEL 6.4 even now, instead of 6.6 or 7.0)
Seconded, the support lifetime of Ubuntu makes it woefully inadequate for use in an enterprise environment. I get that the hip startup scene wants the latest and greatest, but I work in the medical industry and rock-solid stability and availability are more important than anything else - we still have a couple Windows Server 2003 R2 and Windows XP systems that we haven't finished decommissioning yet, along with a couple SQL Server 2005 installations.
When we made our first major Linux deployment this year there's no way I would have picked anything but RHEL/CentOS, we have critical services running on these systems that will be in use for a long time, and playing the upgrade dance in 5 years even (shorter than it sounds) is not an appealing thought.
Honestly, Ubuntu doesn't even try to focus on your type of usage you've defined.
Given your companies pattern of doing its first deployment of Linux this year, and needing a very long support cycle - I think it's fair to say that you're looking for the equivalent of a traditional UNIX. Slow moving, with lots of stability and strong guarantees on backward compatibility. Red Hat and SUSE focus on that type of "enterprise computing" - they've grown on doing 'UNIX replacement'.
Ubuntu is aimed more at the (as you put it) "hip start-up scene" or at least the area in the technical spectrum that is about new technologies, concepts such as continuous deployment and cloud computing.
The funny thing is most enterprises have a bit of both those types of computing. Some slow-moving "eggs in one basket" services, but also the need for fast-moving innovative areas. So there's room for more than just one sort of distribution.
A paid RHEL subscription will even give you security updates for point releases, in case your needs preclude from upgrading even to backwards compatible versions (e.g. You can use RHEL 6.4 even now, instead of 6.6 or 7.0)