Assuming there is no heatsinking done on the print board whatsoever, the chip heats up 125 degrees celsius for every Watt of power it has to dissipate. At 7.5mOhm Rds, that means you can run 8 Amps through it to make it heat up by 60 degrees more than ambient temperature (which would make it definitely hot to the touch, but not hot enough to do any harm).
Here's a graph of the above scenario (Y is temperature rise in degrees celsius, X is the amount of Amps): http://www.wolframalpha.com/input/?i=y+ ... %3D0+to+10
Now, this design does have some heatsinking built into it, but I can't say for sure how effective it's going to be. So the heat up is probably even less than the graph shows, we'll have to test that.
My LED strips are around 11 Watt per meter I think, so if you have comparable ones 5 meter would be 55 Watt, or around 4.6 Amps. This should be well within the boundaries of what this module can handle.
The programming lanes on the back are just for emergencies, I intend to write the software in such a way that we can just reprogram them over wifi. I only use the lanes once at the moment, for initial flashing. They are spaced just like dupont wires without the connectors on, so it's easy to temporarily press wires onto the lanes, or solder them on if you want permanent access.