Strongest way to connect loose 20awg wires together
If the joins don't need to be massively flexible (i.e. rely on the wire around the joint to flex rather than the joint itself), to be honest a simple solder splice and heatshrink should do the trick.

Strip about 10mm of insulation off each wire.
Slide at least 30mm of heatshrink tubing over each motor wire.
Take the motor wire and your 5ft wire and overlap the stripped ends. If it's stranded wire, trying to intertwine the strands for strength.
Solder the two wires together, making sure that the wires are well wetted with solder in the process.
slot over the heatshrink and shrink with a hot air gun or hair dryer.

The larger solder area and heatshrink area should provide a pretty solid join. You can increase the length of the heatshrink if you want to 40mm or more to get extra overlap though will limit flexibility.