In this paper we present the first DL cryptanalysis on 4-round Xoodyak and the first related-key DL cryptanalysis on 5-round Xoodyak. We present the first DL distinguishers on 4- and 5-round Xoodoo, and then perform key-recovery attacks on 4- and 5-round Xoodyak using two recent techniques: the partitioning technique and the neutral bits idea. The data complexity of the 4-round DL attack is about 2^23.34  nonces and the times complexity is about 2^23.34 4-round Xoodoo calls. The data complexity of the 5-round related-key DL attack is about 2^22.04  nonces and the time complexity is about 2^22.04  5-round Xoodoo calls.