Using cosmogenic 10Be data to study the period 1423--1980 AD, we identify a previously unrecognized 5 year modulation process that occurs during epochs of low solar activity. In this, the galactic cosmic radiation exhibits a maximum intensity near sunspot maximum, as well as the well-known intensity maxima coincident with sunspot minimum. This demonstrates that the 5 year periodicity previously reported in the power spectra of 10Be and 14C data is not due to atmospheric processes, and allows their physical significance to be studied.