Because you are modulating a full strength carrier with an audio signal? The resulting modulated RF, with full strength carrier, is of greater amplitude than any component of the audio signal, typically. You have added energy to what was previously only a baseband audio signal.

I assume you are comparing the PAPR of the baseband signal alone, with the PAPR of the modulated RF. If so, it makes sense to me. Now, compare it with suppressed carrier single sideband, and PAPR should not be greater than the baseband PAPR.

The 5 MHz signal by which you multiply the BB signal has itself a PAPR of 3 dB as it is a sine with maximum 1 and rms sqrt(1/2).

so in general the modulated signal has a PAPR 3 dB higher than the BB signal if you use the same definition of peak power to average power without averageing the peak power on one period of the RF