How to analyze BJT amp circuit with multiple gains
The 0.9mA is probably an approximation (and a crude one at that) to the 0.877mA figure you reach by assuming Vbe = 0.7V. Knowing the collector current of Q2, which is equal to the emitter current of Q3, knowing the DC current gain of the transistors (which should have been supplied, but you might also assume that you're working with transistors with high enough DC current gain that the base currents are effectively zero and collector current equals emitter current) you can calculate the collector current of Q3. Following, you have a known voltage drop over the 10K resistor, which you can use to calculate the voltage over the 10K emitter degeneration resistor of Q4, to determine its emitter and collector currents. The process for Q5 will be identical, and you'll reach a complete DC solution.