KöMaL 2011 C1091

In the lottery, 5 numbers are drawn out of the numbers 1 to 90. One time, the following numbers were drawn, listed in increasing order: $\overline{ab}$ , $\overline{bc}$ , $\overline{ca}$ , $\overline{cb}$ , $\overline{cd}$ . The sum of the five numbers is $\overline{bcc}$ , the product of the third and second numbers is $\overline{bbec}$ , and the product of the third and fifth numbers is $\overline{eccd}$ . Determine the digits $a$, $b$, $c$, $d$, $e$.