Sprite not working/not being displayed (Python/Pygame)

I think the real crux of the problem is the code is not adding playerSprite to the all_sprites_list. If a sprite is not in this list, the sprite update and paint calls do not include it. At first I thought the initial position of the sprite may be off-screen, so I parameterised the screen dimensions, and positioned the sprite in the middle.

There's a bunch of other indentation issues in the question's code too, but I think these may be from pasting the question into SO.

I cleaned-up and re-organised the code, it seems to run, and pressing Left/right moves the brown box.

I merged both files together to make my debugging easier, my apologies.

import pygame, random

pygame.init()
BROWN     = (205,192,176)
DEEPBROWN = (139,131,120)
CL        = (156,102,31)
WHITE     = (255,255,255)

WINDOW_WIDTH=500
WINDOW_HEIGHT=500

# Setup the pyGame window
size = (WINDOW_WIDTH, WINDOW_HEIGHT)
screen = pygame.display.set_mode(size)
pygame.display.set_caption("Adventure")

class LittleMan (pygame.sprite.Sprite):

    def __init__(self, color, width, height):
        super().__init__()
        self.image = pygame.Surface([50, 75])
        self.image.fill(CL)
        self.image.set_colorkey(WHITE)
        self.rect = self.image.get_rect()
        self.rect.center = ( WINDOW_WIDTH//2 , WINDOW_HEIGHT//2 )

    def moveRight(self, pixels):
        self.rect.x += pixels

    def moveLeft(self, pixels):
        self.rect.x -= pixels

# Create the player sprite
playerSprite = LittleMan(CL, 200, 300)

# Add user sprite into PyGame sprites list
all_sprites_list = pygame.sprite.Group()
all_sprites_list.add(playerSprite);

clock = pygame.time.Clock()
carryOn = True
while carryOn:

    # Handle user input
    for event in pygame.event.get():
        if event.type == pygame.QUIT:
            carryOn = False

        if event.type==pygame.KEYDOWN:
            if event.key==pygame.K_x: #Pressing the x Key will quit the game
                carryOn=False
            keys = pygame.key.get_pressed()
            if keys[pygame.K_LEFT]:
                playerSprite.moveLeft(5)
            if keys[pygame.K_RIGHT]:
                playerSprite.moveRight(5)

    # Update and Reapint the screen
    screen.fill(BROWN)
    pygame.draw.rect(screen, DEEPBROWN, [55, 250, 900, 70],0)
    all_sprites_list.update()
    all_sprites_list.draw(screen)
    pygame.display.flip()
    clock.tick(60)

The LittleMan class does not include an update() function, which all_sprites_list.update() would normally call. I expect you just haven't needed this part yet.

EDIT: More notes on the sprite update() function ~

The sprite's update() function is called by pygame during the all_sprites_list.update() function. So that means any sprite added to this group, has its update run quasi-automatically. Ideally all sprites have an update function, and it handles the look, position and collisions (etc.) of the sprite.

The idea behind this function is to do any updates to the sprite. So of you had a sprite that was moving, this function would calculate the next position, and set the sprite's self.rect. Or perhaps that sprite is animated - the update function would set the sprite's image to the next frame of the animation based on the time.

Obviously all this work can be performed outside of the update function. But it provides a simple and clean programming mechanism for sprite mechanics.