You might consider [`SliceVectorPlot3D`](https://reference.wolfram.com/language/ref/SliceVectorPlot3D.html) with `"BackPlanes"` as the second argument:


    e = {Cos[π x/5] Sin[π y / 4], Sin[π x / 5] Cos[π y/4],  Sin[π x / 5] Sin[π y / 4]};

    SliceVectorPlot3D[e, "BackPlanes", {x, -2, 2}, {y, -2, 2}, {z, -2, 2}]

[![enter image description here][1]][1]


  [1]: https://i.sstatic.net/bnTzo.png