Siahn said:

What are the limits to sending resources to other alliance members.  I know we can send 5 drones in one day to an alliance member.  Are there other limits: by quanity in a day? # of drones in a week? # of drones and quantity of resources in a week? 

The limit daily is set by your Tech Level, as you explained you know you can only send 5 drones daily to an alliance member.  With that the amount that you can send daily is based on 5 x (your tech level).  The tech that determines this is the the Resupply Drone Capacity.

Above is a screenshot of this, I currently can send 2,700 per drone.

This is a screenshot of the different levels and capacities:

The amount you can send is also affected by the VIP - as certain levels, for example VIP 8 gives 30% + carrying capacity!

The amount of drones you can send at one time is affected by your Deployment Limit Tech as well.  If you can send 1, 2 or more at a time.  

I personally had never seen a limit on weekly amounts or to each base, however as reported by @Sparhawk122 (Thank You) he has experienced the following limits

"Maximum of 20 resupply drones a day.

Maximum 37.5k resources per base.

Maximum 3 resupply drones per base per week."

Let me know if you have any other questions about this =)