The potential energy of a particle executing SHM changes from maximum to minimum in 5 s. Then the time period of SHM is:

P.E. is maximum at extreme position and minimum at mean position

Time to go from extreme position to mean position is, $\mathrm{t} = \frac{\mathrm{T}}{4}; \mathrm{where} \mathrm{T} \mathrm{is} \mathrm{time} \mathrm{period} \mathrm{of} \mathrm{SHM}$

$5 \mathrm{s} = \frac{\mathrm{T}}{4} \Rightarrow \mathrm{T} = 20 \mathrm{s}.$