Chia Burgers began operations by opening $115$ restaurants in Western Canada at the end of its first year of operations. By the end of year $2,$ an additional $5$ restaurants were opened. By the end of year $3,$ there were $130$ restaurants operational. At the end of year $5,$ there were $138$ total restaurants. From the end of year $1$ to the end of year $5,$ the number of eat establisments grew at a rate of $\_\_\_\_\_$ compounded annually.