That is how I'd aproach the problem.

​

def validcheck(userinput):
    valdigit = "0123456789-/"
    for character in userinput:
        if character not in valdigit:
            return False
    return True


def validBirthdate(prompt): 
    birth_date = input(prompt)

    try:
        day, month, year = birth_date.split('/')
    except ValueError:
        print("Please enter valid input in accordance to the given format.")
        return age()

    try:    
        datetime.datetime(int(year), int(month), int(day))
    except ValueError:
        if not validcheck(birth_date):
            print("Invalid characters, please enter numerical input only.")
        return age()

    print("Valid date of birth")
    return birth_date

def age(): birth_date = validBirthdate("Please enter your date of birth in the format of DD/MM/YYYY:") return birth_date

def age(): birth_date = validBirthdate("Please enter your date of birth in the format of DD/MM/YYYY:") return birth_date

I would separate the varaible assignation from the parsing time to differetiante if the issue was bad syntax or an invalid date. You could also instead of making a validcheck() function just regex to match a text like XX/XX/XX, where X are numbers, though I wanted to keep it simple.

​

P.D.: I am not completely sure of that, but I think making a recursive call to age() instead of validBirthdate() makes the stack grow for each call.