24AWG Ribbon Cable Connectors
The standard method of using this type of cable with dual-row 2xN connectors is to use crimp pins on the individual conductors, then insert the pins into an appropriate housing.

These housings go by several different names.  On eBay, people refer to them as "Dupont" connectors.  The housings and pins (in cut-tape form) are really quite inexpensive.

However, I need to be able to order from reputable suppliers.  One such is Harwin.  These are readily available from Digikey: Harwin 2x5 housing.  The matching contacts are also available from Digikey: Female Contacts 22-30 AWG.

The Asian suppliers sell these things for almost nothing.  I purchase the eBay versions for my own projects but use parts from Digikey for my customer's projects.