Animal Age Calculator
My two most important remarks concern comments and global variables.



Python is a language that is designed to be easily readable.  Your three comments simply restate the obvious, and are therefore obnoxious or harmful.  (Redundancy simply doubles the burden of code maintenance, as you have to ensure that your comments are consistent with the code.)

The most important kind of documentation in Python is the docstring — and you didn't write any!



The use of global variables makes it difficult to understand and maintain your code.  The presence of a global variable means that a reassignment could have effects beyond the scope of a function.  That defeats one of the principal advantages of packaging code into functions, which is to make it clear what the inputs and outputs are for a particular chunk of code.



Simple rewrite

Your "restart" feature doesn't actually work.  I've removed it in the code below, and am leaving it as an exercise to you to fix it.

import time, random

def comment(human_equiv_age):
    """
    Print a remark based on the human-equivalent age.
    """
    if human_equiv_age &lt; 25:
        print("You're a young cat or dog")
    elif human_equiv_age &lt; 50:
        print("You're a middle aged cat or dog")
    else:
        print("You're an old cat or dog")

def main():
    """
    Ask the user for inputs to an animal age conversion, and print
    the result.
    """
    print("Welcome to the animal age calculator")
    time.sleep(1)
    choice = int(input(
        "Which age would you like to convert? (Enter the corresponding number)\n"
        "1. Human ---&gt; Dog\n"
        "2. Human ---&gt; Cat\n"
        "3. Dog ---&gt; Human\n"
        "4. Cat ---&gt; Human\n"
        "5. Generate a random human age\n"
    ))
    time.sleep(1)
    if choice == 5:
        print("You have chosen to generate a random human age.")
        time.sleep(1)
        print(random.randint(1,122))
        time.sleep(1)
    elif 1 &lt;= choice &lt;= 4:
        input_age = int(input("What age would you like to start with?\n"))
        if choice == 1:
            print("You have chosen Human ---&gt; Dog and the Human age is", input_age)
            chrono_age = input_age
            human_equiv_age = 11 * chrono_age if chrono_age &lt; 3 else 22 + (chrono_age - 2) * 4
            output_age = human_equiv_age
        if choice == 2:
            print("You have chosen Human ---&gt; Cat and the Human age is", input_age)
            chrono_age = input_age
            human_equiv_age = 15 if chrono_age == 1 else 25 + (chrono_age - 2) * 4
            output_age = human_equiv_age
        if choice == 3:
            print("You have chosen Dog ---&gt; Human and the Dog age is", input_age)
            human_equiv_age = input_age
            chrono_age = human_equiv_age / 11 if human_equiv_age &lt; 33 else (human_equiv_age - 22) / 4 + 2
            output_age = chrono_age
        if choice == 4:
            print("You have chosen Cat ---&gt; Human and the Cat age is", input_age)
            human_equiv_age = input_age
            chrono_age = 1 if human_equiv_age == 15 else (human_equiv_age - 22) / 4 + 2
            output_age = chrono_age
        time.sleep(1)
        print("Your new age is:", output_age)
        time.sleep(1)
        comment(human_equivalent_age)

main()


Some additional remarks:


Python supports double-ended inequalities, like 1 &lt;= choice &lt;= 4.  Note that I haven't used that feature in the comment() function, though.  Can you see the bug in your code, and why I didn't use double-ended inequalities there?
Make the distinction between calendar years and human-equivalent years clear.  Those two quantities don't really have the same units, and that made your comment() function messy.
Your formulae for choices 3 and 4 are the same.  Surely, the Cat→Human calculation is not the inverse of the Human→Cat calculation.


There are other changes I would make, but I'll leave it at this to keep the review simple.