Consider x and y positive integers. Which is the smallest positive integer value that $|11x^5−7y^3|$ could assume?

Question

Consider x and y positive integers. Which is the smallest positive integer value that $|11x^5−7y^3|$ could assume?

I tried to separate in two cases. First, with $11x^5\geq 7y^3$. Clearly, the smallest value is 4. The second case $7y^3>11x^5$. I did some euclidean divisions, but I couldn't get anywhere.