Many times you just have to learn as you go. It is a fascinating experience.
So it looks like you have several 12v 7Ah lead acid batts hooked in parallel which equals 49Ah total. It would be wise to have fuses between each battery so that if one battery goes bad and shorts, it won't ruin all the other ones.
YOu probably already know, that if you want your batteries to last for years, you should practice taking out no more than 25 percent of your total AH capacity. Which in your case, 49Ah divided by 4 is about 12.25 AH. (or;around 147 WH)
So, your one 13watt cfl light bulb combined with your inverter losses will be around 20watts total being spent-- which would be about a total of 7.4 hours running the one light bulb at a safe 25 percent AH discharge with all 7 batteries hooked together.
Your voltage reading is somewhat low. You should test the voltage of each batt separately (disconnected) after the are 'rested'(no load/charge) on them for a couple of hours. Full charge should be around 12.7/12.8 if the battery is new. If it is old it will be somewhat less. You may be getting a bad battery.
You may want to buy a (120vac) battery charger and charge them and see what voltage is 'full charge'. (mine shows about 14.2v is full charging at 6 amps///charging at only 2 amps though, it is about 13.2 volts is full charge)
But with your small 5W PV (which is actually more like 3W in full sun) the amps will be so low, It may be difficult to know what is full charge. (my quess is around 12.
That inverter probably spends about 4 watts on idle if it has a little cooling fan on all the time.(I actually put a switch on the top of mine that turns the 2watt fan on/off)
I have never needed to turn the little fan on even with running my Tv/and dvd player (total=160Watts or 13Amps) since it never even gets warm. Ive been doing this for about a year. The aluminum is always cold where the power FETS are even after running it for hours like this.
Now, my 600W rated inverter only uses 2W idle instead of 4W!
I only did this because I couldnt stand the noise of the little fan while watching TV and also I NEVER use over 14 amps at any one time.
(BTW, I am not encouraging anyone to do this!! It could burn yours out!)
YOu really need to get more solar panel. -Keep having fun.