compatibility of sites created in Dreamweaver 5.5 with subscription to Dreamweaver CC

I fully understand your problem, and it is true that in absolute terms, as @Nancy OShea  says, we have to take into account that the web has evolved and that today it meets new standards that did not exist at the time of DW CS5.5.

However, as @BenPleysier  and @L e n a point out, at the time there were specific DW features that have since been removed. This could possibly cause artifacts, or no longer match dialogs, if you were to open these documents from a modern version of DW...

But, what I was getting at with my comments is not to worry about this at all. ... if you, or your users, visit your current sites, you are happy with the result... then there is nothing to worry about.

Don't worry, there are no hidden springs that will eject your content out of the web... it will remain as it is, always searchable and will always satisfy users, certainly not as perfectly as it could be from a smartphone, or any other very modern device, but it will remain accessible to any browser, new or old.

I would like to be able to ask this kind of question in a few years... I admire your approach, and as Ben says, please don't hesitate to come back to this forum if you have questions

adding to what @BenPleysier said, you must also consider some forgetten features that DW 5.5 must had... my memory can play tricks on me, but it seems to me that there were also things like widgets, and the use of the SPRY library, ...

Rebuilding those sites is not a consideration.

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To be honest, that's like watching your boat sink in 6 ft of water.  😭

CS5 came out in 2010.  That tells me your sites are a decade or more behind current web standards.  And in all likelihood they are not keeping pace with the modern web or providing mobile & tablet users with a good experience.  Google penalizes sites that are not mobile-friendly. 

If you're unwilling or unable to modernize your sites every 5-8 years as required, you should hire someone to help you.  There's not much to be gained from upgrading your software if you don't also upgrade your sites with a new layout and functionality.

As @BenPleysier said, Dreamweaver CC supports DWT Templates if that matters to you.  But it also supports Bootstrap which can help you jump start a whole new website that works on ALL devices.  Another option might be to start over with an online site builder like Wix, Webflow or WordPress. 

Whichever choice you make, do it with eyes wide open to the fact that the web is constantly changing.  And you need to keep changing with it.

Just my 2 cents.

If Template features are your main concern, then you will have no problem in upgrading to newer versions of Dreamweaver.

The main difference between CS5.5 and CC21 is the loss of serverside modules.