Yes you can install it alongside either under High Sierra or Mojave via VirtualBox 6.1. This will allow you to run both macOS and Linux OS concurrently, by virtualizing Linux in VirtualBox without needing to reboot. You can then truly have the cake and eat it too and the Mac Pro 2009, if you have the 8 core version, has more than enough power to run both macOS and LinuxOS together.
While I don't have Linux running on my own Mac Pro, I do have it running on both my MacBook Air 2014 as well as my modern gaming PC. Both are running Ubuntu Focal Fossa 20.04.2 which is the most popular Linux OS distro out there alongside Mojave on my Air and Windows 10 on my gaming PC.
I highly recommend the VirtualBox route, because it supports drag and drop and cut and paste between what's running on VirtualBox and macOS, so if you simply want a more modern internet experience while keeping some legacy Mac apps running and creating content, you can create them in macOS and then send the stuff over using a Linux OS to get sent out over the internet, because Ubuntu 20.04 and other distros based on the Focal Fossa kernel will be supported until 2025! Also with VirtualBox, you can create as many virtual machines your hard drive/SSD allows to test drive each one of them. Linux is so light on computer resources that you can run them as a virtual machine and not even feel that is slow.
Hope this helps.
How to Install Ubuntu 20.04 on a Mac using VirtualBox (2020 Version) - YouTube