<<PolylogTools`

modsh = (#//CreateTensor//sh//flatTensor//Expand)&;

I51[x_,y_] := G[y, 0, 0, 0, 0, x,1];

(I51[x,y]//CreateTensor//del//Expand) - ( ((-TensWedge[Li[{2},{x}]//modsh, Li[{4},{y}]//modsh] +TensWedge[Li[{3},{x}]//modsh, Li[{3},{y}]//modsh] -TensWedge[Li[{4},{x}]//modsh, Li[{2},{y}]//modsh])/.CiTi[w___]:>Tens@@(ElTens/@{w})))

I51[x,y] + I51[x,1/y]//CreateTensor//del//Expand

I51p[x_,y_] := I51[x,y] + I51[x,1/y];

Li6[x_] := -G[0,  0, 0, 0, 0, 1/x, 1];

(I51p[x,y] + I51p[y,x])/2 - (5/2) Li6[x y] - (1/2) Li6[x] - (1/2) Li6[y]//CreateTensor//sh//flatTensor//Expand