No issue at all, in principle. There are a few things to consider, though...
If you're making a commercial product which will have to go through EMC testing, it might yield worse emissions if both supplies' switching events happen simultaneously, as the resulting switching noise can add constructively and push the overall emissions higher. The opposite can also be true! Sometimes it's better to synchronise them together, sometimes not.
If you cascade two supplies, the overall efficiency is affected. Say you have two supplies each of which is 80% efficient, and they're joined together. Power drawn from the second supply incurs losses in both, so you only actually get 64% efficiency overall. Try to draw as little power as possible from supplies which are further down the chain from the main supply to the board. So, for example, if your circuit draws the most power from the 12V rail, then the circuit you suggest would be fine. If it draws the most power from the 5V rail, you might like to consider generating the 12V supply from 5V rather than the other way around. (Or perhaps not in this case, as a circuit that can generate a stable 5V from 4.5-6V is likely to be less efficient than a buck or boost converter).