The constant power assumption is not realistic, because the panel will simply not put out 5mW regardless of load.
An ideal constant power source hooked up to a capacitor will charge a capacitor without limit to an ever higher voltage, because it keeps putting out energy and the capacitor has to keep storing it, thereby becoming more and more charged.
Even the most crude model of the situation has to take into account the limiting process: that the voltage on the capacitor will not exceed the applied one, and so the charging has to slow down as the capacitor reaches the target voltage, and therefore the power flowing to the capacitor has to diminish.
We're better off constructing a schematic of the situation based on the equivalent circuit model. If you substitute values into this, it can be subject to calculations or simulation:
simulate this circuit – Schematic created using CircuitLab
Of course, you have to somehow work out the values for the components of this theoretical model which match your given solar panel.
According to this model, things are somewhat complicated. The solar cell can generate electricity when it's unloaded. When the load C1 is open, current still flows and dissipates energy in RSH and D1. There is also some internal series resistance RS that wastes energy and creates a load-dependent voltage drop.
The presence of D1 can be the basis of a simplified view, since D1 can be regarded as regulating an approximately constant voltage. Suppose that RSH is subject to an approximately constant voltage thanks to D1. This means that a constant current flows through it RSH. Then when we subtract that current from IL, the remaining current is distributed between the RS circuit and D1. D1 dumps whatever the load does not draw, without significantly changing its voltage.
And so, if RSH has an approximately constant voltage, it means that RS and C1 form a simple RC circuit, where we can apply the rule of thumb that the capacitor is around 99% charged after five RC constants (or else use the exponential charging formula to work out the time to reach a specific voltage).
Here is where we can also apply a constant power approximation in a way that is justified, though we don't need it. If the voltage on RSH is roughly invariant thanks to the diode, and since constant current is flowing into this node from the current source, it means that the power being delivered by the internal current source is roughly constant. (Constant current times constant voltage.) Some of this power ends up stored as energy, integrated over time into C1, and the rest of it is wasted in dissipation through RS, RSH and D1. Once C1 stops charging, all of the power is thereafter wasted in just RSH and D1.