There are a few ways to approach this. You can use the integrate rate equation for a first order reaction, but an easier way (in my opinion) is to use the formula F = 0.5n where F= fraction remaining and n = number of half lives that have elapsed. In this particular question, we will be solving for n.
First we will find the fraction remaining.
initial moles = 5.2x1024 atoms x 1 mol/6.02x1023 atoms = 8.64 moles
moles remaining = 0.54 moles
Fraction remaining = F = 0.54/8.64 = 0.0625
F = 0.5n
0.0625 = 0.5n
log 0.0625 = n log 0.5
-1.20 = -0.301n
n = 4.00 = number of half lives that have elapsed.