One way would be to design a circuit as follows:
1.) Use a PIC or other microcontroller device capable of operating the 555 timers spoken of below. Use 2 power supplies, one for each desired current output.
2.) The 1st 555 timer will be set up in monostable mode configured to provide a 30 second voltage on pin 3 when a voltage from the PIC is applied to pin 2 of the 555. A relay is set up on pin 3 which, when it goes high (voltage is applied to it) allows the 10 mA from your supply to flow to the experimental load. After the 555 counts 30 seconds the voltage will cease to be applied to the relay via pin 3, cutting off current flow into the load. The PIC will then apply ground to pin 4 momentarily ensuring this happens.
3.) The second 555 timer which is hooked up in ASTABLE mode to provide the pulses of 5 second duration. This is also hooked up to a relay in the same manner (you would make sure this relay would be rated above 400mA, of course) Program the PIC to shut this down after the 10 pulses ends. It will also be supplied with a separate supply only this one regulated to the desired 400mA
You can also accomplish the above (without having to program a PIC) by setting up switches to actuate the timers and shut them off again. On the 555 pin 2 is the trigger which turns them on, pin 4 is reset which stops them, and pin 3 is the output pin. Note that with the 555 in astable mode you are basically using it as an oscillator whose frequency is determined by the values of the supporting components. Have a look at the data sheet for more info.