All the owner's manual would tell me:  Processor type • Intel Core i3/i5/i7 series • Intel Dual Core series • Up to 8 MB cache depending on processor type

It doesn't look like it can take the G Pentium CPU.

Optiplex 5040 SFF Owner's Manual

Also, Google the socket types for the CPU's; they're likely different.

Welcome to the Dell Community  @beastykato 

Intel Core i5-6500 CPU:

http://www.cpu-upgrade.com/CPUs/Intel/Core_i5/i5-6500.html

Even if it would work why would you want to downgrade???

Intel Celeron G3930 CPU:

http://www.cpu-upgrade.com/CPUs/Intel/Celeron_Dual-Core/G3930.html

Best regards,

U2

@beastykato 

That's correct:

If you look at the "Upgrade" chart the G3930 will upgrade to 7th gen CPU's.

Regards,

U2

Lol right the confusion was the Intel chipset officially supports 6th and 7th gen.  However, Dell neglected to add 7th gen support to their bios on the 5040.  So, I can put the i5-6500 from the Dell into the gaming PC with the g4560 or g3930. 

I unfortunately can't swap the G processor back into the Dell to replace the i5 I'm pulling out tho.

I'm pulling the i5-6500 out for my gaming PC.  And was putting in a cheap weaker CPU into the little SFF Dell.  

The G3930 won't work.  I ended up calling Dell tech support.  The PC only accepts 6th generation (Skylake) processors.  The G3900 would work in that case.  So, that's why my g3930 and 4560 wouldn't boot, they are 7th generation.