Dear Rabbi would you please explain why only five of the festivals of HaShem is listed in the ten Words/instructions of the new tablets that Mose brought down from Mount Sinai Shalom from South Africa
Shalom from Eretz Yisrael. First allow me to clarify that Shemot (Exodus) 34 as written in the title of your question does not describe the Ten Commandments. However, it does describe what was told to Moshe Rabenu after his descent from Mt. Sinai after having received the second set of Tablets. Nonetheless, your question is still valid. Why indeed does the Torah only mention three of the five festivals? The Seforno in his commentary on the Torah explains as follows: Before the mentioning of the Festival, the Torah warns us not make cast metal idols from which people thought to achieve material gain. The festivals are mentioned here as examples of Mitzvot from which material gain will stem if observed. The festivals follow the agricultural cycle of the year. The Torah starts with Pessach which falls in spring which signifies the beginning of growth and material wealth. Shavuoth is called here "katzir" the time of reaping while Sukkot is called here "Chag Ha'asif" the festival of harvest. In the context of material benefit, Seforno explains the other Mitzvot mentioned here as well.