Try playing without looking at the fretboard, as it seems like that may be why you're forced to put your fingers down in a certain order. When you just memorize how your fingers are sort of "locked into place" for a specific chord, you'll find that it's a lot easier to play them one after another. You said that you've just started playing--don't expect to be a professional right away, it takes a lot of time and a lot of practice. Just stick with it, and don't lose faith 
I'm not sure if what you're doing now is the best method of practice. Try playing through ALL of the chords in a random order, not just two chords back and forth. I'd also recommend learning some really basic three-chord songs (look into Creedence Clearwater Revival, that kind of group) so that you can play along with them. I've also found that learning to sing and play at the same time helps with this sort of thing. You also don't want to limit yourself to just those 5 chords; learn as many as you can. Find songs that you like and find their chord patterns and play backup guitar if you don't want to play lead (which you don't seem to want to do).
That's a lot of unorganized information, hopefully you can take something useful from it! Don't hesitate to ask if you've any more questions,
Lou
edit: for bands to look into, look that the "public books" section here, that's what helped me learn to play and sing at the same time.