How can an SDR recover a high-frequency signal? How can software-defined radios operate at high frequency?

The Nyquist rate dictates that you need to sample at twice the frequency to fully recover the signal. If my signal of interest is modulated at $2.5 \,\rm{GHz}$, doesn't my SDR need to sample at $5 \,\rm{GHz}$ to fully recover and demodulate the signal of interest?
The high-frequency (RF) section of an SDR is all analog. Typically, the analog receiver downconverts the RF signal to an intermediate frequency that is within the Nyquist range of the ADC. As Stanley points out, you can also do bandpass sampling, though that is less common, in my experience.