The sum of 17 consecutive numbers is 289. The sum of another 10 consecutive numbers, whose first term is 5 more than the average of the first set of consecutive numbers, is:

Given, sum of 17 consecutive numbers = 289

$$=$$>  Average of 17 consecutive numbers = $$\frac{289}{17}$$ = 17

According to the problem,

The first term of the another 10 consecutive numbers = 17+5 = 22

$$\therefore\ $$Sum of the another consecutive numbers = 22+23+24+25+26+27+28+29+30+31 = $$\frac{31\left(31+1\right)}{2}-\frac{21\left(21+1\right)}{2}=\frac{31\times32}{2}-\frac{21\times22}{2}=496-231=265$$

Hence, the correct answer is Option C