Check My Calculation

 hi max,

 the first thing that came to mind when reading your post was, is there any way to go with a 12vdc bulb in your application? you should be able to find an automotive bulb with the proper ratings.

 if the use of 12vdc bulbs is out of the question then, i would take actual readings with my meter to see what the measured input and output are. i'd especially be concerned with the metered inverter draw from the battery both idle and while powering the bulb.

 we can test these low currents safely with our meter in line from battery output to inverter input. the measured inverter draw is really going to be the make or break on this setup. with your digital multimeter, use the 10amp option. (even the $10 meters are surprisingly accurate) see what the current draw is on that inverter. we know our 5 watt bulb will account for about 420ma and anything over will be inverter losses. we may be disappointed to find that the measured draw on the inverter is much higher.

 i would also check the pv production the same way-when it's nice and sunny can we see production in the approx 1amp or better range?

 these readings (more so the inverter measurements) will give you much better raw data to work with.

 we may be on the big size with that 110ah battery and would think a 25ah might work out better with the limited charging source available. (less self discharge losses and higher input to amphour ratios)

best regards, dave

5 watts x 6 hours a day / 12 volts nominal = 2.5 amphours per day.
(In retrospect, I should have included the fact that watts are watts. A watt doesn't know the difference between voltages. Besides when using an inverter, the 120 vac would not be in the equation because its actually coming from the batteries. Thats why I used 12 volts nominal in the equation above and not 120 or 110.)

115 amphour battery x 2.2% = 2.5 amphours.
(Again in retrospect. What your using from the batteries, I assume at night, is only within the top 5% of battery capacity. This shoud give you way more than 4 days without sunshine.)

4 - PV modules, .350 amps @ 12 volts.
4 hours of equivalent full rated charge per day.
4 x .350 x 4 = 5.6 amphours per day PV.

A surplus of 3.1 amphours PV per day. Not including inverter or wire loss inefficiencies.
(Last, these inefficiencies could add up to as much as a 15% loss. 15% of 3.1 still leaves a surplus of about .5 amphours.)