Python 2, 117 113 108 107 106 105 bytes

from random import*
def f(n):a=['']*5;exec"i=randint(0,(n>44)+(n>59)<<1);a[i]=(a[i]or 0)+1;"*1000;print a

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Returns a reversed list (bottom first)

Python 2, 117 113 108 107 106 105 bytes

from random import*
def f(n):a=['']*5;exec"i=randint(0,(n>44)+(n>59)<<1);a[i]=(a[i]or 0)+1;"*1000;print a

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Returns a reversed list (bottom first)

Version inspired by the stackoverflow answer in the comments (edgecases are more likely):

Python 2, 129 bytes

from random import*
def f(n):a=sorted([1000]*5+sample(range(1001)*5,(n>44)+(n>59)<<1));print[y-x or''for x,y in zip([0]+a,a)[:5]]

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Python 2, 117 113 108 107 106 bytes

from random import*
def f(n):a=[0]*5;exec"a[randint(0,(n>44)+(n>59)<<1)]+=1;"*1000;print[v or''for v in a]

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Returns a reversed list (bottom first)

Python 2, 117 113 108 107 106 105 bytes

from random import*
def f(n):a=['']*5;exec"i=randint(0,(n>44)+(n>59)<<1);a[i]=(a[i]or 0)+1;"*1000;print a

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Returns a reversed list (bottom first)

Python 2, 117 113 108 107 bytes

from random import*
def f(n):a=[0]*5;exec"a[randint(0,2*((n>44)+(n>59)))]+=1;"*1000;print[v or''for v in a]

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Returns a reversed list (bottom first)

Python 2, 117 113 108 107 106 bytes

from random import*
def f(n):a=[0]*5;exec"a[randint(0,(n>44)+(n>59)<<1)]+=1;"*1000;print[v or''for v in a]

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Returns a reversed list (bottom first)