Among $1, 56, 111$, \ldots~the smallest possible $$N$$ that satisfies the two conditions is $$56$$. 
$$N$$ is a two$$-$$digit number. When $$N$$ is divided by $$5$$, the remainder is $$1$$. When $$N$$ is divided by $$11$$, the remainder is $$1$$. The smallest possible value of $N$ is~\uline{~~~~~~~~~~}~.(Adapted from $$2016$$ AMC $$8$$ Problem, Question \#$$5$$) 

$$51$$ 
$$54$$ 
$$56$$ 
$$61$$ 
$$67$$ 