Powering Several Electrical Components from Single Three-Phase 240V AC Supply
Is it dangerous to step down from such a high voltage to reach 5 V DC?


No, this is very common. All "wall-wart" adapters do this. Use a properly certified product to do this.


  Are there potential stability issues? 


No, but you'll have slight imbalance between usage of phases, this won't cause any issues. If your application requires a 3-phase supply then that will certainly dominate (I assume your 24V DC and 5V DC parts draw relatively little current)

As an example, the house in which I live is in a country where almost all houses have a single phase 240 V AC supply. This house had a three-phase supply fitted as it was intended to install an electric home heating system that needed a three-phase supply. However one of those phases would additionally supply all the other household appliances, including 32 A circuits for electric ovens, showers etc. In fact I have gas powered heating installed and only use one of those three electrical phases, the other two have 0 A drawn from them. That's a fairly extreme imbalance. I encounter no stability issues.


  Does it not make sense to convert between three-phase and single-phase power?


If you have a device that works from a three-phase supply it is entirely appropriate to use a three-phase supply.


  Could a power supply simply be connected directly to the 240 V AC source?


Yes. This is normal. By directly I assume you mean through an appropriate distribution panel with RCD/GFCI protection and permanently wired to a suitable outlet conforming to all local regulations.


  Or possibly some sort of custom step-down transformer?


That's just one particular type of power supply. So yes.