Timothy is trying to solve a riddle set by his friend.  \hspace{0pt}  After thinking for some time, he decided that the answer must be "$7$". His reasoning is as follow: $5$ is smaller than $8$, so regrouping must have taken place. In that case， $8$ +~\uline{~~~~~~~~~~}~= $15$. The answer must be $7$.     Is Timothy\textquotesingle s answer correct? If not, what do you think is the correct answer? Show your working! 
Overseas Competition->Knowledge Point->Counting Modules->Permutations and Combinations->Combinations Overseas Competition->Knowledge Point->Combinatorics->Number Puzzles->Number Puzzles (vertical forms)