rechargeable power source for 5x7 LED Matrix

Learning how to decide on the power needs for a project.

I am driving a 2 color LED Matrix(CSM 57281EG) with two MAX7219s, one for the green and one for the orange.
The datasheet on the driver gives me this bit of information.

The upper limit for power dissipation (PD) for the
MAX7219/MAX7221 is determined from the following
equation:
PD = (V+ x 8mA) + (V+ - VLED)(DUTY x ISEG x N)

My power dissipation is calculated to be .1W or .287W depending on Iset.
I would like the project to run for at least a few hours.

I am needing a 5 volt rechargeable source.

I looked at .33F 5.5V supercap. Energy from supercap(J) = .5(Capacitance)(Voltage Squared)
To calculate time using my max PD I did .1Watt = 4.125J / time
This led to about 40 seconds.

I am looking for many many more seconds.

I have 3.7 volt rechargabe AA sized batteries but would have to run 2 in series. but I was hoping for something smaller and equal to the voltage needed.

Any reassurance that I am doing this right and any suggestions for rechargeable sources would be appreciated. Thank you for your time.

0.287W at 5V = ~57mA. AAA-size NiMH re-chargeable cells have a typical capacity ~ 800mAH at some specified low current. So 4 cells will give you ~4.8V-5V and a theoretical run time of ~14 hours (in practice perhaps 10 hours).