I recently downloaded "ubuntu-15.10-desktop-amd64. I haven't installed it yet. My laptop has an Intel i5 processor should I be concerned or should I search for a different version ? I haven't installed it yet.
I run an Ubuntu-based Linux distro on a Core i5 computer, zero problems....
I run an Ubuntu-based Linux distro on a Core i5 computer, zero problems. AMD64 is recommended for newer computers, as most computers run processors based on AMD64.
The installer is a "live medium," meant to be installed on a dvd, meaning that if it doesn't work you needn't install it, since you can try it before you install.
Short version: Yes! Do it!