The picture will help, but when you say white, do you mean the pigment of the leaf color? Or does there look like there's something white growing on the leaves? Maybe a powder-like substance?

Sounds like powdery mildew. It spreads by rain or if you splash the leaves when you water your plants. Generally it starts at the bottom of the plant and gets higher and higher as the powdery mildew spreads up the plant. When it happened to me, it took about a month before it took over the entire crop. I tried pulling off the lower leaves but it didn't work, so I'm not sure if there's a solution other than tearing down the plant and starting over (hopefully in a new location). I wouldn't plant cucumbers in the same location next year.

"White" brings 2 things to mind - sun scorch or powdery mildew. A photo would help. But I am also concerned about your limited water schedule - 5 mins of drip 3x a week is not much water at all. And what have they had in the way of supplemental nutrients as a nutrient deficiency is also a possibility.

Dave