This is legal language, which is a type of technical language, and in the wise words of a fellow-member as written in his profile,
Legal writing is a hyper-technical job in that a legal writing cannot be left capable of admitting two or more meanings. It must throw one and only one meaning, even if one reads it in bad faith.
Unfortunately the contractual sentence you quoted here appears to open up space for multiple meanings. You are generally recommended to get a legal opinion of what exactly that sentence means, but looking at it from a logical perspective in conjunction with your statement that your monthly fee is going to be 5000 dollars, I would suggest that the important phrase in the sentence is
a monthly fee of US Dollars 5,000
which can be clearly read, based on the additional information you supplied, as specifying, guaranteeing and limiting your monthly salary. That is not ambiguous, although we are likely at first reading to be confused by the "monthly fee of 5000 USD for each day..." part. The monthly fee part makes it clear you will be paid 5000 USD (and normally no more than 5000 USD) for each month. You also appear to be guaranteed that monthly 5000 as long as you fulfill the terms of your contract. However, reading it as "5000 USD for each day" as some members seem to have done is not warranted, because the phrase "monthly fee" has been clearly used here. So there can be no ambiguity that 5000 is for the whole month. Moreover, you can earn the full 5000 by working on just one day of the month only if the company needs your services for that particular day alone.
So what does
"for each day agreed as worked under this Agreement"
It seems to be concerned with what constitutes a day's work and a month's work under this agreement, and implies that for you to be eligible for the "full 5000", both you and your employer must be able to agree that you have 'worked' each 'agreed' day of the month (as specified in the terms and conditions of your employment, which you have not mentioned here.) If you happen to miss 1 or more 'agreed' days there shall be a proportionate cut in the payment. It also seems to lay down the understanding that a 'daily rate' for any odd number of days that may come before/after a full month shall be calculated as a 'fraction' of the monthly 5000 USD. I now see this is the way at least 2 other members have interpreted it in the comments section.
Explanatory, hypothetical example: if you are contractually expected to work 25 days a month, then you might be eligible for the full 5000 USD only if you actually work 25 days in the month. Moreover the 'daily rate' compensation for any number of odd days worked in addition to a completed month, or the 'daily deduction' of salary for any number of days not worked in a month might be calculated as 5000/25 = 200 USD in this particular hypothetical case. That means that if you were to leave the company 6 days after a completed month, your fee for those 6 days would be 6 x 200 = 1200 USD. Maybe you could work only 23 days in a particular month? If so, you shall be paid 2 × 200 = 400 USD less than the monthly 5000. Some countries and companies would even calculate that "nominal daily wage rate" as 5000/30 = 166.67 USD, assuming 30 days to every month, even if you are expected to work only 25 days per month according to your contract, because the employee is considered "under contract" for all 30 days of the month in such cases.
So you can see that so much of the meaning depends on how exactly your job responsibilities, nature of work, hours of work, allowed leave and days off, calculation of daily wage rate, etc are defined in your job contract.
Note too that "for each day agreed as worked under this Agreement" might even be simply a fancy legal writing convention that means "for the duration of this contract" ("for as long as this contract exists and you fulfill this contract, however many days that may be.") Again, that basic assessment is just based on my reading of the isolated sentence you quoted in your question. You would definitely need to take the help of a lawyer to interpret the whole document in context, from the correct legal point of view.