Connection a Low Amp wire to High Amp wire
If the load only draws 350mA then that is what the wire will carry.
The potential problem arises that if the 5A circuit is fused at current that is much higher than the thin wire can handle without overheating, you could potentially have a fire or a burn if the thin wire becomes shorted. So generally it's &quot;better&quot; to keep the wires similar size or separately fuse any taps off of a bus bar or thick wire right where it is tapped off.