Question 1107244
.
96.


<pre>
    Obviously, this 2-digit number is of the form N =x6, where x is the "tens" digit and 6 is the "ones" digit.


    Since "it gives a remainder of 5 when divided by 7", it means that  N-5 is divisible by 7.


    N-5 is the number of the form  x1  (referring to N = x6), i.e. N-5 is ended by "1".


    Among 2-digit numbers there are only TWO of the form x1 that are divisible by &. They are 21 and 91.


    91 is the largest, and it produces  N = 96.
</pre>

Solved.