Lim as x approaches 0 of sinx/x is x/x=1, because when x is small, sinx=x and cosx=1.
Lim as x approaches 0 of sin3x.cot4x/cot5x=sin3x(cos4x/sin4x)tan5x=sin3x(cos4x/sin4x)(sin5x/cos5x). When x is small, this becomes: (3x/4x)(5x)=3/4*5x=15x/4. As x goes to 0 this expression also goes to 0, so the limit is 0.