Help building a small solar charging kit
There are 2W poly-silicon based panels that are designed as "battery maintainers" for storage of cars.  They work well even in winter at latitudes of 40+ and a rainy environment behind a windshield (direct experience).  So very low insolation and lots of light reduction going on.  This basically offsets leakage and keeps the battery from going flat which can be bad for longevity.

Most panels are rated for an insolation that corresponds to mid-latitude US and summertime conditions this is known as STC (Standard Test Conditions) so that little 2W panel mentioned above may have been producing ~ only 1W peak at best.  Keep in mond that was only ensuring that the battery is charged for the next spring.

In equatorial Kenya, especially at higher elevations the insolation will be 3 - 4X of the scenario above. So closer to 2.5 W for much longer during the day.  The total Energy (W*Hr) in Kenya vs. winter temperate example will be much much higher simply because the light will be available for longer in the day.  Insolation maps for the all areas are available.

Is your 5W sufficient?  well more than sufficient to keep the battery charged.  If it's enough for all the units (like lights etc.) that need supplying is another thing because that depends upon demand.  I would recommend that you look at that side of the equation first to allow you to supply parameters for the design.

Since cost is so extremely constrained, here is one approach to consider.
The smaller the panel the better.  With a small panel your charging becomes almost an non-issue and is safe.  But then the issue shifts to how do I prevent the battery from being overdrawn so that the small panel has a chance to recharge it the next day.  the design shifts to having a simple monitoring circuit that allows only so much power to be drawn and then protects the battery (with an over-ride for emergency).

Of course there are other ways of doing this with different balances of panels, batteries and circuit sophistication and cost.  The social elements are probably the main area where your project is going to fail or win.

Here are some numbers:


Nokia feature phone uses a BL-5CB battery 800mAh @ 3.7 V -> 3 W*h -> call it 4W*h with inefficiencies.
White LED lamp draws 10W @ ~ 1000 Lumens (60w incandescent = ~1000 Lumens) at 4 hours/night = 40 Wh -> 50 Wh with inefficiencies.

note this is totally un-realistic, as this LED would be very very expensive.
a reading light need not be ~ 1000 lumens either.
so lets cut this in 1/2 -> 25 Wh needed

worst case scenarion 25 Wh + 5 Wh = 30 Wh might well be doable with a 5W panel and 6 hours a day of sunlight.