Why is my program not looping even if the counter works?

You can simplify and start to make the code reusable by putting it into a function. Also, it's a good idea to make it pythonic and remove all the ; that will only serve to confuse the reader as to what language they're looking at.

def login(name, age):
    password = input('Enter your desired password: ')
    print('Registration successful')
    tries = 5
    for i in range(tries):
        print(' Login ')
        login = input('Enter password: ')
        if login == password:
            return True
        else:
            print(' Wrong password')
            print(f'{tries-1-i} trial(s) left ')
    return False

name = 'Bob'
age = 12
if login(name, age):
    print(' Welcome ', 
          'Account Information: ', 
          f'Name: {name}', 
          f'Age: {age}',
          sep='\n')
else:
    print('Account locked')

Example Output:

# Success 1st try:
Enter your desired password: password
Registration successful
 Login
Enter password: password
 Welcome
Account Information:
Name: Bob
Age: 12

# Success 3rd try:
Enter your desired password: password
Registration successful
 Login
Enter password: pass
 Wrong password
4 trial(s) left
 Login
Enter password: pass
 Wrong password
3 trial(s) left
 Login
Enter password: password
 Welcome
Account Information:
Name: Bob
Age: 12

# Fail:
Enter your desired password: password
Registration successful
 Login
Enter password: pass
 Wrong password
4 trial(s) left
 Login
Enter password: pass
 Wrong password
3 trial(s) left
 Login
Enter password: pass
 Wrong password
2 trial(s) left
 Login
Enter password: word
 Wrong password
1 trial(s) left
 Login
Enter password: pasword
 Wrong password
0 trial(s) left
Account locked

I got this working.

def login():
    counter = 1;
    x = 5;
    for i in range(5):
        print(' Login ');
        login = input('Enter password: ');
        if login == password:
            counter -= 1
            print(' Welcome '); 
            print('Account Information: ');
            print('Name: ',name);
            print('Age: ',age)
            break; 
        else:
            x=x-1; 
        if x==0:
            print('Account locked');
            start();
        else:
            print(' Wrong password');
            print(x,' trial(s) left ');
def start():
    for i in range(1):
        global password
        password = input('Enter your desired password: ');
        print('Registration successful');
        login();

start();