• Instead of importing all of random, you could import only random.choice (from random import choice)

• Instead of using escape sequences to print single quotes ' and double quotes ", you should, for the sake of readability, do this:

  print("Something in 'quotation' marks") print('Something in "quotation" marks')

  Note the use of single and double quotes to denote strings-

• Conditional statements can be improved, instead of if letter_guess in word: and then if letter_guess not in word:, use an if-elif (-else) setup. See Rewritten.

• I am really tired, but I'm sure there's better ways to implement game logic here-

Rewritten

I've rewritten your code to be easier to follow and read. I've avoided using functions (but seriously, learn functions, they're helpful).

from random import choice

# Removed WORD variable since you don't really need it
word = choice(('apple', 'oracle',
                     'amazon', 'microsoft'))

# Removed correct variable since it points to word and is therefore not
# needed

clue = word[0] + word[::-1][0]    # Simplified slices
# Removed redundant letter_guess = '', since 
# this is overwritten in the while loop
word_guess = ''
store_letter = ''
count = 0
limit = 5

print('Welcome to "Guess the Word Game!"')
print('You have 5 attempts at guessing letters in a word')
print("Let's begin!")
print('\n')    # print('\n') prints a newline,
                  # not a blank line, maybe use
                  # print()

while count < limit:
    letter_guess = input('Guess a letter: ')
    count += 1
    # Moved count += 1 here so count doesn't have
    # to be incremented twice
 
    if letter_guess in word:
        print('yes!')
        store_letter += letter_guess
  
    else:
    # if letter_guess not in word:
        print('no!')

    if count == 2:
        print('\n')
        clue_request = input('Would you like a clue? [y / n] ')
        # Added "[y / n]" to make it clear the 
        # user can only use those responses
        if clue_request == 'y':
            print('\n')
            print('CLUE: The first and last letter of the word is: ', clue)
        elif clue_request == 'n':
            # Changed to elif
            print("You're very brave!")
    
print('\n')
print('Now its time to guess. You have guessed', len(store_letter), 'letters 
correctly.')
print('These letters are: ', store_letter)

word_guess = input('Guess the whole word: ')

# Removed useless while loop (both if and else 
# statements break out of the loop)

if word_guess.lower() == word:
    print('Congrats!')
else:
    # You don't have to write out a whole
    # elif condition, just use else-
    print('Unlucky! The answer was,', word)
    break

print('\n')
input('Press Enter to leave the program ')
# This last input may be redundant if your only
# option is to leave