Is it Islamically permissible to take some types of food supplies from the hotel where I work, given the lack of promotion despite deserving it, the low salary, the high cost of living, and having five dependents to support?

The needs of the questioner, the high cost of living, or his lack of promotion do not justify him taking what is not rightfully his, betraying trust, or unlawfully devouring people's wealth. He is entitled to demand payment for his extra work or refuse to perform it, but not to take compensation without the hotel owner's knowledge. He should seek another job to increase his income in a permissible way.