Let, $A_1,\mathrm{}{A}_2,\mathrm{}{A}_3,\mathrm{}\dots \dots ,\mathrm{}{A}_{11}$ be $11$ A.M.’s between $28$ and $10$
$\Rightarrow 28,A_1,\mathrm{}{A}_2,\mathrm{}\dots \dots ,\mathrm{}{A}_{11},\mathrm{}10$ are in A.P

Let, $d$ be the common difference of A.P.
Also, the number of terms $=13$

$\Rightarrow 10={\mathrm{T}}_{13}={\mathrm{T}}_1+12\mathrm{d}=28+12\mathrm{d}$
$\Rightarrow d=\frac{10-28}{12}=\frac{-18}{12}=\frac{-3}{2}$
$\Rightarrow$ Number of integral A.M.’s are $5$