How many 5-letter words can be formed out of the letter of the 'EQUATION', if repetition of letters is not allowed?
Well, we just want to permute a subset of size 5 out of the bigger set of 8, say points or letters. This can be done in $8 \times 7 \times 6 \times 5 \times 4 = 6720$
However, the answer in the book says $15120$. What is the flaw here? or the flaw is in the book answer sheet?
Is it possible the question is asking about the word "EQUATIONS"? The solution in the book is $9!/4! = \space_9\text{P}_5$, which would be the correct answer for a $9$-letter word with no repeating letters.
If the question is as you stated it here, then your answer is correct, being $8!/3! = \space_8 \text{P}_5$