1. Do you have the "Monday blues"?

2. Do you have the blue Monday?
3. Do you have Monday blues?
4. Do you have blue Monday?
5. Do you have blue Mondays?

(Which one are correct?)

Do you have the monday "blues"?

#1 is correct. "Monday blues" is in quotes because it is the name of a condition.

Out of the five phrases you mentioned, all of them are grammatically correct and can be used to express the idea of feeling down or a bit melancholic at the start of a workweek.

However, there are subtle differences in their meanings:

1. "Do you have the 'Monday blues'?" - This phrase is in common usage and is often used to inquire if someone feels tired, unmotivated, or down on Mondays in general.

2. "Do you have the blue Monday?" - This phrase uses the singular form of "blue Monday" and implies a specific Monday when someone might be feeling down or low. It is less common but still understandable.

3. "Do you have Monday blues?" - This phrase drops the definite article "the" and refers to the general concept of feeling down or unmotivated on Mondays. It is the most commonly used variation.

4. "Do you have blue Monday?" - This phrase is similar to the second one, but uses the singular form without an article. It is less common but can still be understood in context.

5. "Do you have blue Mondays?" - This phrase suggests that the feeling of being down or low on Mondays is a recurring event. It indicates that Mondays, in general, tend to have this effect on the person.

Each variation is valid, but "Do you have the 'Monday blues'?" and "Do you have Monday blues?" are the most widely used.