Can I do an MS in CS in USA after a 5-year integrated MSc degree in CS?
The rules are theirs, not mine, but I would interpret what you say as indicating you would be ineligible. Your current university doesn't consider your degree to be a &quot;glorified undergraduate degree&quot;, of course, nor will a university that you apply to.
There is some resistance generally for accepting people who already hold an &quot;equivalent&quot; degree even if there are no firm rules. This is to allow others the opportunity to advance when there are limited slots available. The question that would be asked, even if only in the minds of some, is &quot;Why do they want to do this?&quot; and you would need a compelling reason to overcome that sense.
One possibility for a compelling reason is that the MSc part of your degree seems to be practical, not theoretical. Applying to a highly theoretical MS in the US might seem like something new to readers of your application. Maybe enough to overcome any reluctance.

And, for the record, you are almost certainly qualified to apply to a doctoral program in the US. This would probably come with a paid position as a TA (or similar). Likely also no costs for tuition if you are a TA.