Can I replace a 135mm/5mm QR hub with a 10mm-diameter IGH? I have a bike whose rear wheel has "quick-release 5 x 135mm". Will I be able to replace this rear hub with an in-gear hub that has "Length 135 mm, Axis diameter 10 mm" (this is the N380 hub)?
With a quick release system there are two potential width measurements: the inner width of the axel (which a skewer fits into) and the outer width of the hollow axle.  The "quick-release 5 x 135mm" likely refers to the width of the quick release skewer diameter/width and the "Length 135 mm, Axis diameter 10 mm" is referring to outer diameter of the axel which fits into the frame.

For your hub swap, the outer diameter of the axel is matters as this is what fits into your frame.  As rear quick release systems used a 10 mm rear axel, the hub should fit. 

Finally, if your frame is a quick release frame, you likely have vertical dropouts.  These are not always compatible with internally geared hubs.  You should ensure your frame is compatible with your internally geared hub.