J=5/2;
Jp=Table[KroneckerDelta[j,j'],{j,-J,J},{j',-J,J}].Table[KroneckerDelta[m,m'-1]Sqrt[(J-m)(J+m+1)],{m,-J,J},{m',-J,J}];
Jm=Table[KroneckerDelta[j,j'],{j,-J,J},{j',-J,J}].Table[KroneckerDelta[m,m'+1]Sqrt[(J+m)(J-m+1)],{m,-J,J},{m',-J,J}];
Jx=h(Jp+Jm)/2 ;
Jy=h(Jp-Jm)/(2 I);
Jz=((-I)/h)(Jx.Jy-Jy.Jx);
Jx //MatrixForm
Jy //MatrixForm
Jz //MatrixForm