The 5th house is know as the house of discrimination and intelligence. It shows our ability to make clear logical distinctions and discriminate between truth and untruth. This quality was highly developed in the mind of Swami Vivekananda, the great spiritual leader and expounder of Vedanta, a principal branch of Vedic philosophy.
To examine intelligence in the chart, we need to examine the 5th house, 5th lord and the significator of intelligence, Mercury. Notice how, in Vivekananda's chart, the 5th lord, Mars, is strong in its mulatrikona sign of Aries, and aspected closely by the great benefic Jupiter. Jupiter is also the ruler of the 1st and 4th houses, forming two raja yogas with Mars - as the 1st and 5th, and the 4th and 5th lords. This shows his astute, and sharp intellect. His name, Vivekananda, means 'joy through discrimination.' The 5th house also relates to education, especially non compulsory education, like college level. Jupiter's aspect to Mars also reveals his great interest in philosophy, which he was what he studied in college. Jupiter is the planet of philosophy. The strength of Mars in his chart also shows his exceptional strength and courage, which were traits he was known for as evidenced in the following quote:
"All power is within you, you can do anything and everything. Believe in that, do not believe that you are weak... You can do anything and everything, without even the guidance of any one. All power is there. Stand up and express the divinity with you... Arise, awake, sleep no more. With each of you there is the power to remove all wants and all miseries. Believe in this, that power will be manifested."
- Swami Vivekananda
Natal Chart of Swami Vivekananda