Most of pirkei avot is very specific about attribution of various ethical teachings, with the notable exception of the 5th parek, mishnayot 1-19, which are all anonymous.
Is there a tradition of who is to be credited for these teachings?
R. David Zvi Hoffman has a fascinating monograph called HaMishnah HaRishonah uFelugta deTannai, in which he traces the development of various mishnayot, from their earliest forms to what we have today.
He dedicates one section to the development of Masechet Avot. He claims here that the earliest part of Avot consisted of the first part of our first perek, the later part of our second perek, and parts of our fifth perek, in particular those mishnayot dealing with the numbers ten, seven and possibly four. He also claims that these mishnayot were authored by Rabbi Akiva.
His thesis is that Rabbi Akiva was tracing the development of the mesorah until his day. Thus the relevant mishnayot from our perakim one and two list the chain of tradition from Moshe until Rabbi Akiva's own teachers - the students of R. Yohanan ben Zakkai.
The reason for the focus on the number ten at the start of what we call the fifth perek is because there were ten generations from the Anshei K'nesset HaGedolah until Rabbi Akiva's teachers.
Bottom line: according to R. David Zvi Hoffman, the nucleus of what is now known as the fifth perek of Avot was most likely written by R. Akiva.