The grey system installation disks are machine specific. A Mac will not boot from a system that is earlier than what it shipped with.
Sounds like you have another Mac that may be close.
The icon you selected is the A1181, there were 17 versions of this model starting in 2006 and going to 2009
the 2006 had
Pre-Installed MacOS:X 10.4.6 (8I2025)Maximum MacOS:X 10.6.8*
the 2009 had
Pre-Installed MacOS:X 10.5.7Maximum MacOS:X 10.11.x*
So we HAVE to know the exact machines we are talking about here so we can get on the same page to solve your problem.
Find the serial numbers and plug them in on this link to do that
https://everymac.com/ultimate-mac-lookup/