I want to know the best way to express the result of reduced liquid. Example; 5 quarts reduced to 3 Cups. Should it be expressed as ratio or percentage? How do I do the calculation?
There is no single answer to this; it depends on the context and the intent of the recipe in which the reduction is being performed.
Most reductions are expressed as a very approximate percentage, such as "reduce by about half" or "reduce by about two thirds."
Sometimes, you may specify a target amount if that is what is important. "Reduce to about 1 cup."
Lastly, sometimes you specify the outcome desired, as in "reduce until thick and syrupy" or "reduce until the sauce coats the back of a spoon."
Your specific example of five quarts to three cups is very extreme. Probably you want an outcome based description, not a percentage. When specifying by percentage, it is usually for more basic sauce reductions such as a pan gravy after deglazing. Still, the way you have written it is perfectly clear; there is no reason to calculate a percentage if that is your actual intent.
You can express it in ratio form. In your case, it'd be 'three twentieth'. Though usually the expressions are more round such as half, fifth, or tenth and then diluted back if needed.
For example, the famous demi-glace sauce refers to reduced to half (demi) sauce (glace). Some cultures refer to tomato paste based on the reduction ratio (third, or quarter).