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Hello and welcome! My name is ***** ***** I am a licensed attorney and will try my best to help with your situation. There may be a slight delay in my responses as I research statutes or ordinances and type out an answer or reply, but rest assured, I am working on your question.
Who do you actually pay your water bill to? the landlord or the water company?
Is this part of your lease that you have to pay the bill within 5 days?
Do you have any friends or family close by where you live?
Ok, the reason I ask about family or friends is that the simplest way I see to resolve this is for you to leave checks with someone locally who can drop a check in the mail the day you are notified about the bill or even go pay it personally on your behalf.
The other option I see is for you to keep a credit balance on the account.. If your bill is fairly regular, you could pay a month in advance and then your account would just show a credit balance each month.. So if your water bill is $40 a month, you pay $80 one month and you run a $40 credit that gets applied to the next month's bill and you just then continue to stay ahead by making normal payments of $40 a month each month to keep that credit balance going...
However, under a legal doctrine called the "mailbox rule" as long as you get your payment in the mail postmarked prior to the due date, it is considered timely paid regardless of when it is actually received. So you could dispute any late fees if they are being charged as long as you have proof of mailing on or before the 15th.