Crossing Number of $K_5$ on the Tubular Neighborhood of a Trefoil Knot

The crossing number of a simple connected graph $ G$ is the minimum number of edge crossings of $ G$ over all drawing of $ G$ . It’s well known that on the sphere the crossing number of the complete graph $ K_5$ is $ 1$ and on the torus it’s $ 0$ .

What is the crossing number of $ K_5$ on the tubular neighborhood of a trefoil knot?

My intuition is that it’s still $ 0$ , but I’m having trouble showing this.