It would help to create a table (spreadsheet) and list all the items connected to across the battery supply. Then list the max and min current they draw. Sum the currents and you are likely to see what is consuming the battery's current.
As jremington has said you will need to get the average current to less than 5mA.
Your spreadsheet should show which culprits are loading the most. Also you will see how far you are from the target of <5mA.
You can create the spreadsheet while awaitng DMM (current meter delivery) 
Don't forget that the Nano could be used to turn peripherals off and it can put itself to sleep. Also LEDs alone are likely to consume more than your 5mA current budget.
Here is a link that may help: [GUIDE] Using Arduino Nano for battery-powered projects