Why does the Torah insert the first "Mikem" before "Chamishah"?
Rashi: To teach us that even the weakest 1 among us will pursue the enemy.
From the word 'Mach' which means 'weak'. See also Ba'al ha'Turim.
If five will pursue 100 of the enemy, then 100 will pursue 2,000. Why does the Pasuk say 10,000?
Rashi: Because one cannot compare many who fulfill Torah to few who fulfill Torah. 1
Da'as Zekenim #1 (3): The prayer (Hadar Zekenim - merit) of a Tzibur is better.
Da'as Zekenim #2 (3), Hadar Zekenim, Rosh citing R. Tam, Moshav Zekenim: The verse means that 100 groups of five, they will chase 10,000. In both cases, everyone chases 20.
Riva: Some say that "Revavah" is 2000. If so, in both cases, everyone chases 20. 2
Riva: When two 3 chase, they invigorate each other.
Five weak Yisraelim will chase 100, and 100 average or strong Yisraelim will chase 10,000 (refer to 26:8:1:1 - PF).
See Sifsei Chachamim. -Why does Rashi mention fulfilling Torah? Perhaps it is to teach that this Brachah is only when it is a Mitzvah to chase, but not in an optional war. (PF)
This also resolves the calculation in Devarim 32:30 - "one will chase 1,000, and two will chase Revavah"; in both cases, everyone chases 1000 (PF). However, Riva rejects this, for in Shoftim 20:10, "Revavah" is 10,000.
Having already written "v'Naflu Lifneichem le'Charev" in the previous Pasuk, why does the Torah repeat it here?
Rashi: To teach us that they will fall before us in a most unconventional manner.
Ramban, Moshav Zekenim #1: The previous Pasuk is speaking on the battle-field, where they will pursue the enemy as they begin to flee and kill them by the sword, whereas the Pasuk now adds that after the enemy have fled the battle-field, Hashem will grant Yisrael the courage to give chase to far superior numbers, 1 and not only will they chase them, but the five will succeed in killing the hundred.
Ramban (citing Ibn Ezra): It is an indication that they will fall time and time again.
Seforno: The previous Pasuk refers to Yisrael pursuing the enemy outside our territory, and the enemy falling miraculously at the Hand of Hashem. 2
Moshav Zekenim: One hints to in the days of Yehoshua, and one hints to in the days of David.
Our verse says that five will pursue 100, and 100 will pursue 10,000. Devarim 32:30 says that one will chase 1,000, and two will chase 10,000! And there it implies that the enemy chases Yisrael. If so, the Midah of punishment exceeds Midah Tovah!
Da'as Zekenim #1 (3), Rosh citing Ramban: Also Devarim discusses Yisrael chasing them. The Torah says that they should ponder - how could one, i.e. Shimshon, chase [and kill] 1,000 Plishtim, and two, i.e. Yonason and his youth, chase 10,000, if not that Hashem did all this?!
Hadar Zekenim: Also Devarim discusses Yisrael chasing them, i.e. Adinu ha'Etzni (Shmuel 2:23:8), i.e. David. He should have killed 1,000; he killed only 800 due to the sin with Uriyah (Mo'ed Katan 16b).
Riva citing R"M of Kutzi: Devarim says that the enemy should ponder that "b'Acharisam", in the days of Mashi'ach, one Yisrael will chase 1,000, and two will chase 10,000.
Da'as Zekenim #2 (3), Rosh: In Devarim, the enemy chases Yisrael but does not kill them. 1 Here, Yisrael chase the enemy and kill them. Hadar Zekenim, Riva citing R. Tam, and Rosh and Moshav Zekenim - it says here "v'Naflu Lifneichem le'Charev." Rosh - in both places, when more chase, each chaser chases five times as many as when fewer chase.
Moshav Zekenim #1: If Devarim discusses the enemy chasing, when many Yisraelim sin, it is worse (so each enemy chases more Yisraelim). If it discusses Yisrael chasing, the merit of Rabim is greater. Even though we do not find that two are considered Rabim, when people flee, everyone flees.
Moshav Zekenim #2: Here it says that five Yisraelim can chase100 enemy officers, and each officer has 1000 slaves and servants.
Moshav Zekenim: If so, why was David pained that he killed only 800 at a time, and not 1000 (Mo'ed Katan 16b)? R. David - he was pained that he could not chase 1000.