That biasing regime (Fig.2) is basically a collector feedback common emitter amplifier. You may just as well take the feedback from the collector of Q5 for a more conventional looking approach or connect it to the output to avoid pulling the bias current through R2. This type of collector feedback dc biasing is good for being stable with temperature variations. An increase in temperature reduces Vbe which tries to alter Vc leading to a change in Ib (via the collector feedback resistor) which acts against the initial attempt of Vc to change keeping the dc biasing pretty temperature stable.
The problem with collector feedback dc biasing is that it is highly dependent on the beta (hFE) of the transistor. The dc biasing of a potential divider biased common emitter amplifier is far less dependent on hFE.
In Fig.2 you can calculate Ic from (15-1.4)/1k = 13.6 mA.
13.6 mA through the 220R emitter resistor gives an emitter voltage of of about 3 V above the negative rail and a base voltage of about 3.7 V above the negative rail.
Now you need to know the hFE of Q5 to calculate its base current. Let's assume it has a hFE of 200 giving a base current of 13.6 mA/200 = 68 uA.
Now the base biasing resistor should be sized to have 14.3-3.7 volts across it and 68 uA through it yielding a base bias resistor value of 10.6/68 uA = 155.9k. The 14.3 V results from my suggestion of connecting the feedback resistor to the collector of Q5 which is 0.7 V below 0 V.
For a dual supply amp it is important to keep the dc offset at the output as low as possible to keep the dc current through the loud speaker very low and so to cater for an actually unknown Q5 hFE it would be a good idea to replace R1 with a 22 turn multi-turn trimmer and adjust it for an accurate 0 V output dc bias. For a single supply amplifier the output dc bias is not so critical because it would be blocked by a large output dc blocking (ac coupling) capacitor.
The voltage gain of the circuit in Fig.2 is R2/R3 = 1k/220R = 4.5
A voltage gain of 4.5 means that the ratio of the dc voltage across R2 to the dc voltage across R3 is 4.5 resulting in about 3 V across R3. This limits quite significantly the negative (and as a result the positive) output voltage swing because of transistor saturation and so I would suggest increasing R2 or reducing R3 to increase the gain which will reduce the dc voltage across R3 allowing a larger ac voltage swing at the output. Of course you'd then need to recalculate the value of the base bias resistor or just readjust the pot if one is installed.
A series input capacitor is required to ac couple and prevent the dc level of the input signal from affecting the dc bias levels in the circuit.