I think Alain that the 358 and 324 are too far away from the rails.
I would suggest the LMC66x series that are really Rail to Rail, low consumption op-amps. Used them alot. And since the output of the op-amp would always be above ground at least 0,7 volt (Vbe drop), there is no worry about 0 current. It is obtainable (almost!). Enjoy (life, circuits, software, whatever!)
Ioannis
P.S Note that transistor and may be the op-amp might have to be supplied with seperate supply above 5V according to the current you would like to obtain.
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