No, you don't need to use the centre tap.
Another question: is the 5A through the current transformer's primary?
If so, you can use a much lower current and simply wrap the wire through the middle several times, for example if you use two turns and have 2.5A, the current transformer will measure the current as 5A.
If you're bothered about accuracy, you'll need to use a high powered variable resistor to trim the current, otherwise it will change, depending on the mains votlage and transformer regulation.
My local supplier sells 6V 20VA transformers, with twin secondaries whcih can be connected in parallel to double the current rating.
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