What you suggest will work, although I didn't look at your specific resistor values to see if you will get the voltages that you intend.
LM317 is designed so that the output voltage can be set by a resistor divider. That is useful when you want unusual voltages. However, 5 V and 3.3 V are very common, so you could simplify your circuit and use fixed regulators. For example, the very common and cheap 7805 regulator could be used to make the 5 V output.
Another issue is that these are linear regulators and will therefore get quite warm at significant output currents. You didn't say how much current you need at 5 V and 3.3 V, but if more than a few 100 mA, a switcher is probably a better choice. For example, if you draw 300 mA from your 5 V supply, the regulator will drop 7 V and therefore dissipate (7 V)(300 mA) = 2.1 W. A regulator in a TO-220 case will probably need a heatsink at that power.
I'd look into using a switcher to make the 5 V supply. Then you may be able to get away with linearly regulating that down to make the 3.3 V supply. Let's say you are drawing 500 mA at 3.3 V. That would only cause 850 mW dissipation in the 3.3 V regulator, which a TO-220 in free air can probably handle. If you do this, make sure that whatever 3.3 V regulator you use will work with the 1.7 V headroom provided by 5 V in.