5. (10 points) The 3rd term of an arithmetic sequence is 14, and the 18th term is 23. How many terms in the first 2010 terms of this sequence are integers.
【Solution】Solution: From the 3rd term to the 18th term, there are 15 common differences, and this difference is $23-14=9$, thus the common difference is $9 \div 15=0.6$.
5 common differences equal to the integer 3, so the 3rd, 8th, 13th, 18th, ..., 2008th terms of this sequence are all integers, totaling $(2008 - 3) \div 5+1=402$ terms;

Therefore, the answer is: 402