I want to develop an application for Windows 7.5 mango OS phone like HTC Mozart, I am already having Visual Studio 2008, will the apps built by Windows Mobile 5 smartphone SDK be supported in a windows phone?
No, the Windows Phone SDK is the only one that is supported. In short, Windows Mobile != Windows Phone.
Also the UI is drastically different and the underlying runtime and .NET framework is also different. You might be able to port the logic of your code across easily to the new SDK, but the UI will need rewriting.
There are also a lot of freedoms lost in the new iteration as "the user is king". This means you need to review what your current app requires and provides to see if it is even a good fit for the new range of phones.