There is some incompatibility, but it is small, you will certainly have to make some adaptations, you even have to convert it into the project files that have changed (I think automatic wheeling).
Now a lot is not very incompatible, it's a different way to do it. As you are accustomed to one thing, the change can scare you, it may seem like you have problems, and it's really just a lack of knowledge. You'll have to decide whether to start using newer versions of the compiler and .Net, which I strongly advise, or whether you'll set everything up to work with older versions.
Some things you may have done in the project may be more incompatible than others, but I doubt that you will encounter major problems, it is rare for someone to do something very different. Of course that can be your case.
VS extensions may not be compatible, you may have to pick up a newer version, or there is no new compatible version.
I could tell you that staying in 2005 is safer, but in practice is the post, staying with software so old and as far as I know not supported anymore is not safe. Go for 2015 already and pay the price of having to adapt. If I had made the updates over time it would be less traumatic. But do not expect anything tragic. You must be a developer, so you must find solutions. If you have specific difficulties post here.
It's not something that just installs and will work, but it's perfectly doable. In the worst case if it does not work, you could try to go back to VS 2005, which I do not advise at all.