Problem

An arithmetic progression has first term $5$ and common difference $d$, where $d>0$. The second, fifth and eleventh terms of the arithmetic progression, in that order, are the first three terms of a geometric progression.

(a) Find the value of $d$.

(b) The sum of the first $77$ terms of the arithmetic progression is denoted by $S_{77}$. The sum of the first $10$ terms of the geometric progression is denoted by $G_{10}$.

Find the value of $S_{77}-G_{10}$.