Are you sure about that? Could it be that it reads 3.2Ah?
If it reads 3.2Ah, that is it's capacity, not the maximum current. SLA batteries often do not state a maximum current on the label, just the voltage and capacity. It might be able to supply 6.4A, for example, but only for 30 mins.
If 3.2A is truly the maximum current, then in order to provide 5A output, the buck converter probably needs to draw around 2.6A from the battery, so no problem.
Unlike a linear regulator (like the one built in to the Nano), the input current required by a buck converter can be less than the output current, when the output voltage is less than the input voltage.
For example, if your buck converter draws 2.6A from the 12V battery, that is 31.2 Watts of power. If the buck converter is 80% efficient (many are better) then the output power will be 25W. At 5V output, that is 5A of current.