Catalysis of the reaction: cyanidin-3-O-D-rhamnosyl-(1,6)-D-glucoside + UDP-D-glucose = cyanidin-3-O--5-O-D-glucoside + UDP.
UDP-glucose:cyanidin-3-O-beta-L-rhamnosyl-(1->6)-beta-D-glucoside 5-O-beta-D-glucosyltransferase activity