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Using a linear amplifier is a very inefficient way to boost the power of an AM signal. You should not expect to get more than 25% efficiency out of it, because in order to achieve a 5W carrier output you will need an amplifier that is capable of 20W (peak).
As suggested earlier, you could disable the modulation in the SSTRAN and use the output as the drive signal to your amplifier, which I would suggest operating either in Class C or E (non-linear). You should be able to achieve upwards of 70% efficiency in that mode. You could also tap the audio prior to the point where it modulates the carrier in the SSTRAN, and feed that to an outboard audio amplifier, if you would like to take advantage of the preamp and limiter in the SSTRAN.
You should check with your country’s telecommunication authority first, because in most countries, operation at that power level would expose you to severe penalties.
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