See the commentary of Likutei Sichos on chapter 5 of Pirkei Avos, with these specific snippets from chabad.org:
Chapter Five: The world was created by means of ten [Divine]
utterances — According to the principles of Torah numerology, five
represents a level of G‑dliness above all limitation,1 while ten
reflects the structure of our finite, material world. The intent of
this chapter of Pirkei Avos is to reveal the G‑dliness which
transcends all limitation within the context of our material
(Sefer HaSichos 5751, Vol. II, p. 772)
So first of all, the whole chapter, including the parts about Avraham and the miracles of the sea later, are to teach us how to serve Hashem beyond limitation, yet within limiation, see further.
ג - עֲשָׂרָה נִסְיוֹנוֹת נִתְנַסָּה אַבְרָהָם אָבִינוּ וְעָמַד בְּכֻלָּם, לְהוֹדִיעַ כַּמָּה חִבָּתוֹ שֶׁל אַבְרָהָם אָבִינוּ.
3. Our Patriarch Avraham was tested with ten tests, and he withstood them all to show how great was our Patriarch Avraham’s love
Ten tests — As mentioned, the number ten reflects the full scope of
our personal potential. Avraham showed his devotion to G‑d with every
dimension of his being.
Ten tests... to show how great was our Patriarch Avraham’s love [for
G‑d] — The purpose of the tests which Avraham underwent — and of the
challenges which his descendants, each and every member of the Jewish
people, confronts — is to bring into expression a more powerful love
for G‑d [beyond limitations], as it is written:13 “G‑d... is testing you to see if you love
G‑d... with all your heart and with all your soul.”
Our Patriarch Avraham — Avraham is described as אבינו, our Patriarch
(literally “our father”). Just as a father bequeaths his estate to his
descendants, Avraham bequeathed his spiritual legacy to the entire
Jewish people. His spiritual legacy empowers each of us, endowing us
with the strength to withstand the challenges we face in our divine
(Sichos Shabbos Parshas Chukas, 5737)
So this part goes together with the intro, that Avraham serving Hashem beyond all limitations of reason was a lesson for us all to serve him that way (that's the same idea of serving him in an unlimited way within the confines of nature).
ד - עֲשָׂרָה נִסִּים נַעֲשׂוּ לַאֲבוֹתֵינוּ בְּמִצְרַיִם, וַעֲשָׂרָה עַל הַיָּם, עֶשֶׂר מַכּוֹת הֵבִיא הַקָּדוֹשׁ בָּרוּךְ הוּא
עַל הַמִּצְרִיִּים, בְּמִצְרַיִם, וְעֶשֶׂר עַל הַיָּם. עֲשָׂרָה
נִסְיוֹנוֹת נִסּוּ אֲבוֹתֵינוּ אֶת הַקָּדוֹשׁ בָּרוּךְ הוּא
בַּמִּדְבָּר, שֶׁנֶּאֱמַר: וַיְנַסּוּ אֹתִי זֶה עֶשֶׂר פְּעָמִים וְלֹא
4. Ten miracles were performed for our forefathers in Egypt, and ten at the Sea. The Holy One, blessed be He, brought ten plagues upon
the Egyptians in Egypt and ten at the Sea. Our forefathers subjected
the Holy One, blessed be He, to ten trials in the desert, as it is
stated: “By now they have tested Me ten times, and did not heed My
Ten miracles were performed for our forefathers — Pirkei Avos is
intended to teach us pious conduct — how to serve G‑d beyond the
measure of the law. What lesson in pious conduct can we learn from
these points of history?
This question can be answered as follows: The fact that G‑d wrought
miracles for the Jews in Egypt made the people aware of their true
identity. Although they were still in exile, the miracles made them
conscious that they were G‑d’s servants, rather than slaves of the
This is also true today. Although we are still in exile, we are G‑d’s
servants, and subject to no other authority. **Our commitment to Him
need not be limited in any way. On the contrary, just as miracles
represent a departure from nature, our commitment can rise above
ordinary mortal constraints.
(Sichos Shabbos Parshas Nitzavim, 5738)
So as we can see, the entire idea of the whole chapter, and Avraham's tests, is to teach us how to serve Hashem beyond our limitations, and the same idea is expressed in the miracles, which are an expression of Hashem that's beyond nature.
So the connection: both the "10" miracles of Egypt (which ten, as mentioend, represents how Hashem is complete even in this world) and the "10" tests if Avraham, both of them mentioned in chapter 5 which, as mentioned above, represents how Hasem is totally removed from the world (see the Sicha there for sources explaining why), are to teach us, and are inherently related to, the idea of serving Hashem beyond all limitations, but still bring that into the limitations of the world, like how to plagues wer miracles, beyond all limitation, but it affected them in a way that even in the limitations of exile, they were able to perceive Hashem, and the same is true of the 10 trials of Avraham, that Avraham showed that he served Hashem with his full human (/even natural) potential.
So: the 10 tests of Avraham = Avraham's full (even natural) potential, and the 10 miracles in Egypt = Hashem's infinite revelation in a way that made even the Jews in exile still, aware of the greatness of Hashem.
Both of the ideas represent how Hashem permeates even our natural/limited being.