Problem powering Arduino Pro Mini

Not sure whether this is the right place to post this. I set up a very simple configuration using:

1 Pro Mini
1 Oled display
6 Peltiers
2 Thermometers
2 0,7A Fans
6 Relays
1 AC-DC adaptor 12V - 50A

The job is only about switching Peltiers on/of in order to keep a constant temperature over a metal plate.

PROBLEM: The sketch runs fine when the Pro Mini is connected to a computer and powered via USB. When I power it through the AC-DC adaptor, using a LM7805 to reduce 12 to 5V, the Pro Mini goes crazy. I tried 12V directly to raw and the pro mini not even blink.

What have I tried so far and did not work:

1- Putting the AC-DV far away from Pro Mini (field interference?)
2- Setting a 2nd AC-DC 5V totally separated from the 12 V, not sharing ground or whatsoever

Any clue about what could be the reason and solution to this problem?

When I power it through the AC-DC adaptor, using a LM7805 to reduce 12 to 5V, the Pro Mini goes crazy.

3.3volt or 5volt ProMini.
Did you connect that 5volt supply to VCC, not to V-in (raw).
And did you use the recommended decoupling capacitors on both sides of the 7805.
Post a diagram.

Thanks for you help.

It is a 5 volt ProMini.
Yes, the 5 volt supply is connected to VCC not to V-in Raw
No i did not use any capacitors on 7805, it is just ground, Vin (12V) and Vout(5v) directly to Vcc on Pro Mini. Where should I place capacitors and which capacitors?

Search Google for the datasheet of the xx7805 you have.
Most need 0,33uF from input to ground, and 100n from output to ground (minimum values), close to the regulator.
The 7805 could oscillate without the caps, and that could destroy the ProMini.

OK, I will do that. Another question: Have you ever experienced instabilities in micro controllers, like the ones from Arduino families, due to electromagnetic fields generated by coils, motors, AC-DC adaptors and other devices placed near by? I am asking because that was one of my hypothesis and then I placed the AC-DC far from the micro controller. But that is so troublesome in my arrangement that I would like to know whether this is reasonable or not. But for sure I will try out the capacitors as you suggested, thank you very much for you help.