Abstract. Let G be a graph. Denote by Lⁱ(G) its i-iterated line graph and denote by W(G) its Wiener index. Dobrynin, Entringer and Gutman gave a problem if there exists a nontrivial tree T and i≥3, such that W(Lⁱ(T))=W(T). In a series of 6 papers we completely solve this problem. This is 5th paper of the series and here we define a class of trees satisfying the above equation for i=3.