(b)
$Mn^{+} = 3d^{5},\ 4s^{1}.In\ presence\ of\ CO\ effective\ configuration = 3d^{6},\ 4s^{0}$.
Three lone pair of back bonding with vacant orbital of C in CO.
${Fe}^{0} = 3d^{6},\ 4s^{2}.In\ presence\ of\ CO\ effective\ configuration = 3d^{8}$.
Four lone pair for back bonding with CO.
${Cr}^{0} = 3d^{4},\ 4s^{2}.\ Effective\ configuration = 3d^{6}.$
Three lone pair for back bonding with CO.
$V^{-} = 3d^{4},\ 4s^{2}.Effective\ configuration = 3d^{6}$.
Three lone pair for back bonding with CO.
Maximum back bonding in $Fe(CO)_{5}$, therefore CO bond order is lowest here.