Coin flip explanation

#1
Hi, I have been wondering about a probability question.

Suppose you have a 50% chance of winning $1 when you flip a coin. You also have a 50% chance of losing $1 when you flip a coin. You keep flipping the coin as many times as necessary until someone is up $5 or someone is down $5. What is your probability of winning $5 dollars, what is your probability of losing $5. I feel like the obvious answer is 0.5. However, I am interested in the way to actually prove this answer is correct or show it is correct with math. Can anyone please help? Thanks!

Also, what is your probability of winning $5 in the same situation, except you have 51% chance of winning the flip and a 49% chance of losing the flip. Thank you so much in advance!