The ULN2003A does not have a power pin. It has a catch diode pin that is common for all outputs. It can be connected to the highest voltage supply that has a load controlled by the ULN2003A.
For example, if you have loads connected from ULN2003A outputs to +5V and to +12, connect the COMMON to +12. Of course each load will be connected between one ULN2003A output (OUT 1 ~ OUT 7) and the respective supply (either +5 or +12).
In fact if your loads are resistive (and have short leads) you could probably leave the pin open, but it does no harm to connect it to the supply as indicated. Connecting it to +5 would be very bad as it could result in overvoltage (via the +12V loads) on the 5V supply, probably breaking something.
Your schematic does not look right, but it's so messy I hesitate to delve into it on a relatively small screen.