Let x be the least number which when divided by 8, 12, 20, 28, 35 leaves a remainder of 5 in
each case, then the sum of digits of x is :

According to question,

$$x$$ is the least number which when divided by 8, 12, 22, 28, 35 leaves a remainder of 5.

Now instead of dividing $$x$$ individually by 8, 12, 22, 28, 35, we can divide by the LCM of 8,12,20,28,35.

Now, $$8=2^3$$

$$12=2^2\times\ 3$$

$$20=2^2\times5$$

$$28=2^2\times\ 7$$

$$35=5\times\ 7$$

So, LCM of 8,12,20,28,35 = $$2^3\times\ 3\times\ 5\times\ 7$$ = $$840$$

So, I can write, $$x=840k+5$$, where $$k$$ is any positive integer.

So, for the least value of $$x$$, $$k=1$$

So, $$x=840\times\ 1+5$$

or, $$x=845$$

So, sum of digits = $$8+4+5=17$$