You have to try and find a data sheet for those relay module to know what their low side current consumption is.
The basic relays (that is without the driver circuit, LED opto coupler etc.) appear to require about 100 mA if it is the same as here: relay
If that is the case, and depending on what nano you have (clone or original), you may just get away with powering the whole thing from the +5v pin on the nano.
The +5V is not the same sort of 'pin' as pins D0, D1,D2 .... A0, A1 etc. which are switched by the microprocessor. Yes, with those pins your are restricted to an absolute maximum of 40mA.
The relay module will have a power supply input and a trigger input. I guess you measured the current consumption at the power supply input. The trigger input should require only a few milliamps, mainly for the optocoupler Led.
The 5volt relay module posted uses about 75-80mA per relay (when active).
A relay input requires 2mA drive current (sink) from an Arduino pin (LOW=active).
If you use a single supply to power the relay module and the NANO (splicing), you loose opto isolation.
Opto isolation requires two individual supplies.
Don't power the relay boards from the 5volt pin of the Nano. You will burn out the USB reverse protection diode quickly.
Writh a HIGH to the pin BEFORE you set the pinMode to OUTPUT.
That stops those modules from chattering during bootup.
Leo..