#sin(theta)# has a period (i.e. a pattern that repeats every increment) of #2pi#

For #sin(theta/2)#, #theta# would need double the incremental distance to reach the repetition point.

i.e. #sin(theta/2)# would have a period of #2xx2pi#

and

#sin(theta/4)# would have a period of #4xx2pi = 8pi#

Similarly we can see that

#sin(5*theta)# would have a period of #(2pi)/5#

Combining these two observations (and replacing #theta# with #t#)

we have

#color(white)("XXX")sin((5t)/4)# has a period of #2pi*4/5 = (8pi)/5#