What kind of source footage are you using in your project? It sounds to me like you may be using a highly compressed format as footage inside of After Effects...
only 5 minutes of cuted parts of other videos with a background music.
Well, have you considered the sources to be the problem? AE still sucks at compressed audio formats (assuming you may imply using MP3 or something) and just as well embeddded audio in compressed formats liek AVCHD is not always to the program's taste. Similarly, compressed audio and video is conformed to the media cache and any performance or corruption issues there might result in invalid output. Definitely investigate that route. also check your options for hardware acceleration in AE and otehr possibly conspicuous things that may interfere, including external third-party CoDec stuff.
Well it would make sense because I am effectively using mp3 backtrack and .avi footages
in your opinion does Adobe premiere pro be better for what a want to do?
ANY real video editing application will be better than After Effects at editing, Premiere included.
There are very few applications that are worse than After Effects when editing video. Microsoft Word is one of them.
The following page probably contains the answer why your playback isn't smooth: