If a coin is weighted so that the probability of heads is five times the probabily of tails, that means :
+) P(head) + P(tail) = 1
+) P(head) = 5P(tail)
Therefore, P(head) = 5/6 ; P(tail) = 1/6
For both head and tail to be flipped, the events must happen together.
Therefore, we have the probabilty that both head and tail is flipped = 5/6 x 1/6 = 5/36.