DIY Solar lamp circuits with 5252F explained?
The correct chip name is QX5252F.

The datasheet of the chip allows up to 6V input, so you can use your 5V panels.

The speed of which the battery will charge is mostly dependent of how much light you would get on your panel.

Unfortunately, the datasheet doesn't provide any information on how the panel are regulated, so to guess, it probably some sort of discrete regulator.

In that case, the voltage of the panels would be at the same voltage as the battery (plus a small dropout voltage of the regulator).

You need then to know the I-V characteristic of the panel to know how much current your panel will provide for this voltage.

Once you know that, you can factor the value for a specific illumination.

To calculate the charge of the battery, it's simply the average current x time - losses.