Ah, sorry, I ignored your first post. It still doesn't boot, correct?
You can certainly boot to your new bootable installer, and reinstall El Capitan, which installs El Capitan over the existing installation, and shouldn't disturb your existing files and apps. The
result should be a good (booting) system.
When you get to that "Reinstall OS X", don't forget to reset the date on your system through the terminal, otherwise the El Capitan install will likely fail with an error (something like "problem during install" or a message close to that). The system clock should correct itself the first time you connect to the internet. The "date" command is just to bypass a minor glitch in the El Capitan installer that has been around for the last 2 or 3 years.
Note: if the reinstall doesn't fix your booting issue, then a full erase/install will be your next step, and you would want to back up your internal drive before the
erase/format, as you would be correct -- you would lose everything that is not backed up.
Your new external
should be OK. I have a Seagate Backup Plus 8TB which refuses to boot, but does work as a Time Machine backup drive, so I have that split into 4 partitions, for a variety of backup uses. Don't know why I can't make a partition bootable, as I (think) I know all the "tricks". Somehow related to the firmware of the device. Hopefully, you do not have one of those Seagates
I'm pretty sure that you won't be able to install a bootable OS X system on a partition on that 5TB, unless the format Scheme (the Partition Map) is GUID. Master Boot Record (MBR) won't work, for example.
Yes, you will need to erase/format if the drive is MBR, and the best choice for Format option is Mac OS Extended (journaled)
Again, the device needs to be formatted GUID. But you can make multiple partitions, if you like, and make one of your choice ExFAT, if you need to share storage with a Windows system.