The CT accuracy class must be equal to or greater than the required CT secondary terminal voltage.
For example, if you had standard 2.0 ohm burden the required secondary CT terminal voltage would be Vs=2.0 ohms x 5A X 20 = 200 Vrms.
If your available primary fault current drives the secondary CT current greater than 20 x 5A, then you would need to go to a higher class CT.
So in the above example, if you had a 600/5 ratio CT, and your primary fault current was 18kA, the CT secondary current would be 150 A, which is 30 X the 5A secondary CT current rating. In this condition the CT will saturate become non-linear. You would then need to go to a higher CT class.
There are other considerations that also come into play, but hopefully this will helps understand the importance of selecting the right CT accuracy class.
Perhaps you are getting class and ratio mixed. For your scenario above, you could use a higher ratio CT (1200/5) to drop the secondary current to 75 amps.
There are a few factors when determining ratio and class:
1.) You should find out what the available short circuit is. If it is 18kA, for example, you want to select a ratio that will reduce the secondary current to personnel and equipment in the event of the full fault. The rule of thumb is to keep it less than 100A, secondary; preferably below 75A. In this case, you would need no less than a 1200/5 ratio. The CT class has nothing to do with this.
2.) The class is determined by burden (or load). The load includes the relays and the CT cables and anything else in between the CT and the relays....like test switches, terminal blocks, etc. If the load is too high, you'll need a higher class CT. Typically, the older E-M relays have a high burden and require higher class CTs. Really long CT cables also requires higher class CTs. If you are using new microprocessor relays and short runs of CT cables (<300' of #10), then you should be able to use C200 class CTs. There are calcs that can help determine all this. Also, the class has nothing to do with CT ratio.