I'll take a stab at this - as I have had the same problem..
when you add a transition premiere begins the transition a few frames (I believe 3) from the end of the first cut and fades into 5-6 frames of of the following cut.
you should know that priemiere just hooks pointers into the source file and doesn't make actual copies of the video as per your 'cut'
so - as you are only working with 5 minuites of video and are probably trying to squeeze every possible second of precious runtime into your final product... and are cutting right to the exact frame where you hit the 'unpause' button.
try advancing 4-6 frames into the beginning of the second cut (most common fix) or 1-3 frames back into the end of your preceeding cut (second most common fix), or a combination of the two
You may lose an overall second or two of runtime but your transitions should be silky smooth.
enjoy
/edit
hmm that looked confusing to me as I reread it so perhaps a picture or two..
original capture (each symbol represents the frames between pauses, each '|' represents where you hit pause)
|1111111111|2222222222|3333333333|4444444444|
so you have an original capture with 4 scenes (10 frames each) - you set your inpoint at the first '1' and your outpoint at the 10th '1' and copy it to the timeline, then repeat exactly for the other three scenes - then you try to transition between scene 1 and scene 2 - if you place the transition at the dividing point you will get (the 'T' is the rendered transition frames)
|1111111111|112222222222|3333333333|4444444444|
...............TTTTTT
so.. if you mixed the scenes up you might see
|1111111111|334444444444|223333333333|334444444444 |
...............TTTTTT...............TTTTTT........ .......TTTTTT
although you 'cut' to the exact frame - the transition effect actually uses a couple of frames prior and after where you marked your in or out point.
hope i'm not confusing you..
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