Question 850049
Question a)  is reasonable, but question b) is not reasonable without knowing more, maybe friction information.  We also must be given how high IS the wall. 



(a)  You are calculating how high up the wall the ladder touches.
{{{y^2+5^2=13^2}}}
{{{y=sqrt(13^2-5^2)}}}
{{{highlight(y=12)}}}.


(b)  We now know how high up the wall the ladder reached in part (a), but we are given no information about the actual height of the wall.  "After painting the top 5 meters...", is meaningless.  Was the wall 12 meters high?  Should the ladder now be adjusted so it would touch 7 meters up the wall?  If this were the case, then one assumption which may be possible is to keep all sides of the triangle describing the three points in proportion.