Can OS X 10.5.8 be installed on a 2.3 GHz Intel Core i7 Mac Mini?
Your Mac mini is probably a Apple Mac mini "Core i7" 2.3 (Late 2012) Macmini6,2. It was originally delivered with Mac OS X 10.8.1.

Neither 10.5 nor 10.6 contain the necessary drivers to support your hardware (especially USB3.0).

Consider installing Mac OS X Server 10.6.8 in an virtual machine using Parallels, VMware Fusion (both non-free) or VirtualBox (free).