I would suggest generating them by hand and create the list later:
import numpy as np
i = np.random.uniform(1.5, 12.4)
j = np.random.randint(0, 5)  # 5 not included use (0, 6) if 5 should be possible
k = np.random.randint(4, 16) # dito
l = np.random.randint(3, 5)  # dito
m = np.random.uniform(2.4, 8.9.)
array = np.array([i, j, k, l, m]) # as numpy array
# array([  3.33114735,   3.        ,  14.        ,   4.        ,   4.80649945])
array = [i, j, k, l, m]           # or as list
# [3.33114735, 3, 14, 4, 4.80649945]
If you want to create them all in one go you can use np.random.random use the range and the lower-bound to modify them and convert them to integer where you don't want floats:
# Generate 5 random numbers between 0 and 1
rand_numbers = np.random.random(5) 
# Lower limit and the range of the values:
lowerlimit = np.array([1.5, 0, 4, 3, 2.4])
dynamicrange = np.array([12.4-1.5, 5-0, 16-4, 5-3, 8.9-2.4]) # upper limit - lower limit
# Apply the range
result = rand_numbers * dynamicrange + lowerlimit
# convert second, third and forth element to integer
result[1:4] = np.floor(result[1:4]) 
print(result)
# array([ 12.32799347,   1.        ,  13.        ,   4.        ,   7.19487119])