$3m^{2}-21m+30< 0$
$A.m<2 , or \ \ m>5$
Option A fails when m=0
$3(0)^{2}-21 \times 0+30=30$
Hence,Option A is false.
$B.m>2$
Option B fails when m=5
$3 \times 5^{2}-21 \times 5+30=0$
Hence,Option B is false.
$C.2<m<5$
when m=3
$3\times3^{2}-21 \times 3 +30=-6$
when m=4
$3\times4^{2}-21 \times 4 +30=-6$
Hence,Option(C) is true.
$D.m<5$
Option D fails when m=2
$3 \times 2^{2}-21 \times 2+30= 0$
Hence,Option(C)$2<m<5$ is the correct choice.