Suppose your city were to send you an incorrect tax bill. You read it, and determine that the assessment is too low. You promptly write a check for the amount demanded. Do you have any obligation to correct the city’s error? Suppose, 5 years later, the city discovers the mistake-are you obligated to pay the amount plus interest? 
That is hard to say. My town has a style of vastly underestimating real estate values for tax purposes. I believe this is to stop a riot from the fact that much of the real estate in town has doubled or tripled in value in the last ten years.
They routinely send out tax bills with assessments of say, $300,000 when the houses are worth more like $700,000 on the market. I have talked to neighbors, and all of our bills are like that.
I don’t know how they would “prove it” retroactively. Our house was a massive fixer-upper. After we did hundreds of thousands of dollars of mostly interior work, I simply refused to let the tax assessor in the door any more. That apparently forces them to use some appreciation calculation based only on the exterior and the last assessment and that seems to have worked greatly in our favor.
I don’t know how they could prove what it was worth at any time in the past. Market values can be finicky and hard to show.
Kind of off topic, but in every place I’ve ever lived, the taxable value of a house - that is, the assessed value the city uses to determine tax - is quite a bit less than the market value of the house were you to sell. In fact, I just got my new assessment in the mail yesterday, and it had gone up to almost half of what we paid for the house 2+ years ago.
I don’t know why it’s that way, but I was under the impression that this was a normal and nationwide practice, not one city or town attempting to stop any riots.
That is not how it works in California. In CA currently the assessed value is the price you paid for the house. There can be adjustments to this value when you make improvements but by and large the assessed value is how much you paid for the house.
The problem I am told is that there are houses in town (some very expensive ones too) that have a tax assessment at or near market value. In fact, the assessments go all over the place and appear to be just made up in a lot of cases. People that have lived there longer than me say it has always been that way.
It makes it kind of hard because people aren’t going to complain about their low bills but, if someone gets more realistic one, it can still be justified by the town.
First, you have no legal obligation at all to correct their error.
Much of this will depend on the law in your specific state.
Some states now send you ‘estimated’ tax assessments several months in advance. Often those states allow only very limited changes once the property tax owner has been notified of the expected tax amount. So that may prevent them from making you pay more.
You are able to challenge the assessed value, and maybe get it changed. Generally, there is a limited time period during which you can do this. Often something fairly short, like 6 months to 1 year from the bill date. In most states, the same time should apply to the taxing body; they can’t come back at you for more money after that time period has expired.
Finally, interest only applies to a debt that is owed. You didn’t owe this increased amount until they notified you of it. So they could only charge interest since the date of the bill, not back 5 years. And since the error was their fault, you would have a good case in arguing for an extension of the time needed to pay it.
Here in Minneapolis, the city instituted a new water billing system many years ago. Due to some problems, many people just didn’t get bills for months at a time. Then they got the system fixed, and people were suddenly getting bills for 12-24 months worth of water service. Big bills! But the city knew it was their fault, and didn’t charge any interest on these bills, and even made special offers to stretch out the payments over several months, again with no interest during this period. Even so, there was a lot of public anger, and some people in the department lost their jobs over it. And it’s considered to have contributed to the defeat of some City Council members in the next election.
If the city tried to increase your tax assessment retroactively to 5 years ago, you could raise an immense stink about it. I can’t imagine any Civil Servant or elected official who would dare to try this.
Here in Arizona our assessed property values seem to be about half of the market value. It was almost exactly 50% for our place, and also for my parents’. I don’t know if that’s a law or something, just an observation.
Same thing in Michigan, I’ve even been told that by a realtor. I just paid my property taxes, the assessed taxable value is about dead-on half what I’d expect my house to sell for.
Not that I’m complaining.