You are talking about two concepts using different terms. The standard financial terms when talking about inflation are "real" return and "nominal" return. "Nominal" return is just the actual mathematical return, not adjusted for inflation or anything else. "Real" return is your return after adjusting for inflation. Since the things you can do with your money now cost 5% more (but see my note below), your "real" return is the "nominal" return adjusted for inflation.
You also describe pre-tax and after-tax returns. Remember, though, that you are only taxed on the gains in your portfolio (and in some cases you are taxed less if you have held your investments for a long period of time). So the formula for real after-tax return R given a nominal pre-tax return r, inflation rate I and tax rate T is:
R = r*(1-T) - I
Or in your example:
R = 10*(1-0.03) - 5 = 4.7%
Note that inflation is a currency measure, and does not necessarily affect individuals in the same way. Your cost of living may go up more or less than inflation over time and will also change because of your circumstances (i.e. if you move to a bigger house your maintenance costs go up, which has nothing to do with inflation).