In Squeak 4.x Smalltalk, it's not golfed, but there is a 299 chars version below
Compile this method in Object:
[| value morph |
value := (((self negated raisedTo: self - 1) / 15) exp exp - 1) reciprocal significand rounded reciprocal.
morph := ToolSet inspect: value.
[(Delay forSeconds: value reciprocal * 5) wait.
morph delete] fork.
(Delay forSeconds: 1) wait]
do: [:exc |
FileDirectory default deleteFileNamed: 'quine'.
(FileStream forceNewFileNamed: 'quine') nextPutAll: thisContext method getSource; close.
^self class newCompiler
evaluate: ((FileStream oldFileNamed: 'quine') contentsOfEntireFile lines allButFirst reduce: [:a :b | a , b])
for: self + 1
Then evaluate '1 quine' where you want.
Each evaluation differs, because it is evaluated with incremented receiver.
evaluate: ... for: self+1 )
The awfull expression computing the value is different for 3 (lead to a Fraction 1/2 instead of Integer 1) and for 5 (lead to ZeroDivide).
The file is deleted when the exception is caught and 5 is returned.
Otherwise, an inspector is opened on the value, the display is refreshed, the process is paused during 1 second before evaluating next quine.
A process for closing opened inspectors after a longer pause is forked.
The source of quine is retrieved via the current context of execution (thisContext method getSource), written, then re-evaluated without the first line (the name of the method). So the second and successive evaluation do not evaluate #quine, but an anonymous (#Doit) method sharing exactly the same contents.
Based on same principles, this less funny example will print 00100 in Transcript then stop when evaluating 1 quine, but it avoids explicit 3 and 5 in source:
quine|v|v:=self highBit-self lowBit.Transcript show:(1bitAnd:v).(2bitAnd:v)=0or:[^FileDirectory default deleteFileNamed:'q'].(FileStream forceNewFileNamed:'q')nextPutAll:thisContext method getSource;close.^Compiler evaluate:((FileStream oldFileNamed:'q')contentsOfEntireFile allButFirst:5)for:self+1