Does the Fifth commandment apply to a biological parent when the child is adopted?
Yes it does. The main reason for the mitzva of kibbuds av v’em is because they are the ones that gave us our life, and caused that we should be able to come to this world. Therefore even in the event that a parent did not provide sustenence for thier child, the child is nevertheless obligated to honor his parents.
Ksav Sofer and Meshech Chochmas Devorim 5-16, Yalkut Yosef Kibbud Av V’em 6-6, The Fifth Commandment pg. 113.