Question

The code given works fine but not with the original code.
I would like the code to offer a number 1 through 5 and only accept a number 1 through 5.
The number choosen Within range would still return random integers.

import random

user_input = raw_input("Enter a number between 1 and 5 : ") 
selected_elem = []

while len(selected_elem) < int(user_input):
    if user_input >= int(6):
        print ("That is not an option...")
    random_elem = random.randrange(1, 10, 1)
    if random_elem not in selected_elem:
        selected_elem.append(random_elem)

print ("Here are the numbers... ")+ str(selected_elem)

Answer 1

UPDATE with OP code posted now:

while len(selected_elem) < int(user_input):
    if 1 <= int(user_input) <= 5:
        random_elem = random.randrange(1, 10, 1)
        if random_elem not in selected_elem:
            selected_elem.append(random_elem)
    else:
        print ("That is not an option...")

Note that if the input to user_input is not a number and int() fails your program will crash (throw an exception). You can graft on the try/except code shown below to deal with that if necessary.

—— Previous answer w/o code posted by OP ————

If you can be sure the input will always be a number you can do this:

while True:
    num = input('Enter number between 1 - 5:')
    if 1 <= num <= 5:
        print 'number is fine' 
        break
    else:
        print 'number out of range'

It will continue to loop until the user enters a number in the specified range.

Otherwise, the added try/except code will catch non-numeric input:

while True:
    try:
        num = input('Enter number between 1 - 5:')
        if 1 <= num <= 5:
            print 'number is fine'
            break
        else:
            print 'number out of range'
    except NameError:
        print 'Input was not a digit - please try again.'

If you don’t want the user to try again after entering a non-number, just adjust the message and add a break statement below the final print to exit the loop.