No it doesn't reduce emissions. The same car fueled with e5 or e10 or any e number will still produce near enough the same quantities of CO, CO2 and other products of combustion. That is a fact that applies whenever a carbon based fuel is burnt.
I believe there is lot of misunderstanding about the Carbon cycle and the part that Bioethanol might help to manage global warming.
In the short term moving to bioethanol produces a recycle time of a couple of years for the burning of bioethanol which converts Carbon to CO2 to the plant life used to produce the fuel to grab the CO2 back from atmosphere.
So in real terms using Bioethanol doe not massively reduce the overall level of CO2 in atmosphere, but it does not increase it either. It's a stabilising tactic not a reducer. But we shouldn't dismiss it, as by not adding any new CO2 we are reducing the strain on Mother Nature
We still need to do more. Conversion to Bioethanol if it reduces New CO2 being released is clearly a good thing, but it also does not address the underlying demand for high grade energy. It would be far better to reduce the numbers of driven miles across the board and other high fuel uses. If nothing else the Covid pandemic has shown that a lot of transport mileage is actually unnecessary.