Jerusalem is mentioned many hundreds of times in the Jewish Bible. As for the Chumash (Five Books of Moses), it’s true that the exact word “Jerusalem” doesn’t appear. The basic reason for this is because it was not yet called by the people “Jerusalem” in any language. Also, the city of Jerusalem had not yet been revealed as “God’s chosen city”.
Under Jebusite rule and even earlier, Jerusalem was divided into two cities. The western part was called “Jeru” (Yere) and the eastern part was called “Salem” (Shalem). Both of these names do in fact appear in the Five Books of Moses: “And Abraham called that place...Yere” (Genesis 21:14) — “And Malki-Tzedek, King of Shalem” (Genesis 14:18).
Around the time of Joshua's conquest, the Amorites consolidated the two halves of the city, and they combined the two names: “Jeru-salem”. From this point on in history, our Bible refers to Jerusalem countless times.
Furthermore, the Chumash refers 19 times to “the place that God will choose” as the center for Jewish life and religion (e.g. Deuteronomy 12:11, 14, etc.). The Prophets Samuel and Gad finally revealed to King David that this “chosen place” is in fact Jerusalem and the Temple Mount.
So these are two reasons Jerusalem isn't mentioned explicitly in the Chumash as the holy city: It hadn’t yet been called that; and it hadn't yet been revealed as such.
Maimonides, writing around 800 years ago, offers three reasons that the Chumash does not explicitly reveal the identity of the holy city:
1. If the nations had learned that this place would express the highest Jewish ideals, they would have united in an effort to occupy and prevent the Jews from ever controlling it. (No comment…)
2. If they had known of Jerusalem's special spiritual stature, they may have tried to take advantage of its spiritual nature by making it into a center of idol worship.
3. Each of the twelve tribes would have desired to have Jerusalem in their borders, and this would lead to disunity.
Once the Jewish People had conquered and divided the land, the above ceased to be considerations.
So, in conclusion, Jerusalem has played a prominent part in Jewish history and writings for many thousands of years.