Power amp element's purpose
C5 is called a bootstrap capacitor as indicated by the other answers but they haven't described the main reason for needing it.

It is to increase the drive to the output transistors Q4 and Q6 and ensure the amplifier reaches its full output capability.

This is in addition to increasing the impedance at the collector of Q3 and increasing its gain as indicated by @Tony Stewart.

Without C5 the most positive that the base of Q4 can be driven is to the positive rail minus the voltage drop in R11 and R12 caused by Q4's base current.

At full output Q6 may need to pass about 5-6 Amps of current.  This will require 100mA or so of base current from Q4.  Q4 in turn will require 1-2 mA of base drive from R11 and R12.  Their combined value of 7.7k will drop 8-10V limiting the maximum positive excursion of the signal at Q6 emitter to about 80v. It will lose about 10volts of the possible output swing and corresponding output power.

With no signal the voltage across R12 will be abut 30V. With C5 in the circuit this voltage be maintained approximately constant even as the signal varies.

This current through R12 will be about 6mA and available to drive Q4 even if the base of Q4 is at the positive rail. The junction of R11 and R12 will swing up to about 120V (30v above the positive rail) during positive peaks of the signal. This can allow Q4 to go into saturation if required ensuring the maximum drive to Q6.

For the negative swing to Q5 and Q7 the same issue does not exist as Q3 can conduct as necessary to drive Q5 fully.

Many amplifier designs use a transistor arranged as a constant current source instead of R11, R12 and C5.  This results in a more symmetric drive to the output transistors and its proponents claim better lower distortion.