Open the tomato paste. If it's gone bad, it will be slightly brown. If not, it's fine but as a PP said, it could have absorbed the plastic of the can liner.

I would toss them. Since tomatoes are a high acid food, the USDA recommendation is to toss after 18 months. Their recommendation for other foods is 2-5 years.

https://ask.usda.gov/s/article/How-long-can-you-keep-canned-goods

I tend to ignore expiration dates in general as long as food looks and smells okay. However I was cleaning out my pantry and found some canned coconut milk and tomato paste that expired over five years ago. Do you think there is any reason not to consume them if they look and smell ok?