Why does the Torah insert the word "Veradfu Mikem" Chamishah"?
Rashi: To teach us that even five of the weakest 1 among us will pursue a hundred of the enemy.
From the word 'Mach' which means 'weak'. See also Ba'al ha'Turim.
If five will pursue a hundred of the enemy, then a hundred should pursue two thousand Why does the Pasuk say ten thousand?
Rashi: Because one cannot compare many who keep the Torah to few who keep the Torah. 1
Da'as Zekenim #1 (in Pasuk 3) and Hadar Zekenim: The Tefilos (Hadar Zekenim - the merits) of a Tzibur are more effective.
Da'as Zekenim #2 (in Pasuk 3), Hadar Zekenim, Rosh (citing R. Tam) and Moshav Zekenim: The Pasuk means that a hundred groups of five will chase ten thousand. In both cases, everyone chases twenty.
Riva #1: Some say that "Revavah" is two thousand If so, in both cases, everyone chases twenty. 2
Riva #2: When two 3 chase, they stimulate each other.
Five weak Yisraelim will chase a hundred, average or strong Yisre'elim will chase ten thousand. Refer to 26:8:1:1 (PF).
See Sifsei Chachamim. Why does Rashi mention keeping Torah? Perhaps it is to teach us that this B'rachah is only when it is a Mitzvah to chase, but not in an optional war (PF)?
This also resolves the calculation in Ki Savo Devarim, 32:30 "One will chase a thousand, and two will chase "Revavah". In both cases, everyone chases a thouand (PF). However, the Riva rejects this, because in Shoftim Devarim, 20:10, "Revavah" means ten thousand.
It seems that he said this in order to resolve the same problem in the Pasuk in Ki Savo (See Devarim 32:30), because here, we can explain that 'When many (a hundred) are chasing, they stimulate each other more (PF).
Having already written "Venaflu 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 and 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 the 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 refers to the era of Yehoshua, and the other, to the era of David ha'Melech.
Ramban: And cause the enemy to become so panic-stricken that a hundred of them will run away from five of Yisrael.
Seforno: See Yeshayah, 66:16. In which case, the current Pasuk is referring to chasing the enemy inside our territory and the enemy falling by our sword.
The current Pasuk writes that five will pursue a hundred , and a hundred will pursue ten thousand. In Ki Savo Devarim, 32:30, the Torah states that one will chase a thousand, and two will chase ten thousand? Moreover, there it implies that the enemy is chasing Yisrael, in which case, the Midah of punishment exceeds Midah Tovah?
Da'as Zekenim #1 (in Pasuk 3) and Rosh (citing the Ramban): The Pasuk in Devarim is also discussing Yisrael chasing the enemy (with reference to the P'lishtim). And the Torah is saying that they should ponder - how it is possible for one - Shimshon, to chase [and kill] a thousand P'lishtim, and for two - Yonason and his armor-bearer - to chase ten thousand, were it not for the fact that Hashem did it.
Da'as Zekenim #2 (in Pauk 3) and Rosh: In Devarim, the enemy is chasing Yisrael but does not kill them, 1 whereas here, Yisrael chase the enemy and kill them. 2
Hadar Zekenim: Also Devarim is discussing where Yisrael (Adino ha'Etzni 3 - alias David) is chasing the the enemy 4
Riva (citing R"M of Kutzi): Devarim says that the enemy should ponder that "be'Acharisam", in the days of Mashi'ach, one Yisrael will chase a thousand, and two will chase ten thousand.
Moshav Zekenim #1: If the Pasuk in Devarim is discussing the enemy chasing many Yisre'elim who have sinned, it is worse (so each enemy chases more Yisraelim), and if it is discussing Yisrael chasing the enemy,, the merit of Rabim is greater. 5
Moshav Zekenim #2: Here it sayhe Torah is referring to five Yisraelim killing a hundred enemy officers - each of whom has a thousand slaves and servants under his command.
Moshav Zekenim: If so, why was David pained that he killed only eight hundred at a time, and not a thousand (Mo'ed Katan 16b)? R. David: He was pained that he could not chase a thousand.
Hadar Zekenim, Riv (citing R. Tam), Rosh and Moshav Zekenim: Hence, the Torah writes here "Venaflu Lifneichem le'Charev". Rosh: In both places, when more chase, each chaser chases five times as many as when fewer chase.
See Shmuel 2 23:8.
He should have killed a thousand, but succeeded in killing only eight hundred - due to the sin of Uriyah ha'Chiti. SeeMo'ed Katan 16b.
Moshav Zekenim: Because, even though we do not find that two are considered Rabim, when people flee, everyone flees.
