5DIII should have good enough high ISO to handle it at 2.8. Street and portraits gives more at 2.8, at least. 1.4 was necessary during low ISO film era
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But, honestly, 5DMIII and any of two lenses for the street and capturing the moment? You should really like the work out. I quit taking 5D series cameras and 50L or standard zoom on the streets long time ago.
And if you want capture the moment on busy street, AF is not the best of the best option.

