In Posuk 5 of Perek 7 in Parshas Va'eira, it says that
Moshe was 80 years old and Aaron was 83 when they spoke to Pharoh.
Why is that important?
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Maayan Bais Has'shoeivah by Rabbi Shimon Schwab Zatzal explains that Moshe and Aharon were telling Pharaoh that his genocidal decrees against the Jewish people were doomed for failure. Eighty years ago you decreed that every boy born shall be thrown into the Nile River to be drowned. Eighty three years ago you ordered that all Jewish boys shall be killed at birth by the midwives. Yet here I Moshe am 80, my brother Aharon is 83 so you see that your decrees of annihilation have failed.
In addition the fact that Moshe was 80 at the time he spoke to Pharaoh that proves that Yocheved was 130 years old when she gave birth.
א*ומרת התורה דווקא פה אחרי שהזקנים עזבו את משה ואהרן ונשמטו, אז התורה מבליטה תראו אלו מנהיגים היו לנו, משה רבינו התחיל את ה'קרירה' בגיל שמונים, ומשה ואהרן הלכו לפרעה לבד, והזקנים נשמטו, 'ויוותר יעקב לבדו', ובכל זאת לא עזבו את המערכה, המשיכו בשליחות מתחילה ועד סוף, אפילו שהזקנים לא הולכים אתם, ואפילו שהם בני שמונים ושמונים ושלוש, ואדם מבוגר בדרך כלל לא מקבל עליו עול חדש כידוע, בכל זאת התמידו בשליחות, שלוחי מצוה לא נזוקין.*
The Torah wants to tell you. Although they were 'forsaken' by all the 'elders' and they were already in their 'eightieth year' which is quite old to start a 'new' career. They still carried on doing the 'message' of hashem even if they had to do it alone.
The peirush of R. David Zvi Hoffmann says that determining their age was necessary to teach us that the elders and the experienced were the ones in whose hands Hashem entrusted the difficult task of redemption.