Can someone help me to find the right transformer for this power supply?
The transformer primary centre-tap is for 115 / 230 V operation. If you don't need it you can just choose the voltage for your region.

The transformer may have been custom wound and you could have difficulty finding a match from any of the large suppliers although +5 V and +/-15 V are common requirements. You can of course use two separate transformers - one for the 5 V supply and one for the +/-15 V supply. Parallel the tranformer primaries to the fused mains supply and connect the common ground points after the rectifier.

If you need to create your own supplies the 7805 (1 A) and 78L15 / 79L15 (0.5 A) voltage regulators would suffice. There are plenty of designs and tutorials on these devices on the web. Pay attention to decoupling capacitors.

Since +5 V and +/-15 V are so common you could also just purchase readymade PSUs. Look out for low noise power supplies so that you don't get audio interference.