The issue here is how long do you steep the tea, at what temperature, and under what conditions do you store the used tea bags? The reason "sun tea" has been discouraged has been because of the likelihood that the tea leaves that are in the bags are contaminated with bacteria such that a long soak in luke-warm water such as that of the "sun tea" causes them to multiply to the extent that they become a serious health risk. Tea leaves are not typically pasteurized during their processing, and may carry viable bacteria and/ or bacterial spores.
If you were to soak the tea bad in warm water not hot enough to get a good bacterial kill initially, there may be enough viable bacteria in the tea leaves to grow during that 5 hour interval such that the next cup may be seriously dangerous (some may divide every 15 minutes, for example). However, if you were to adequately kill the bacteria and spores off by a nice hot soak (for this example, you would need to use a pressure cooker since some bacterial spores are not even killed by boiling water at atmospheric pressure), refrigerate the tea bag afterwards, and then reuse it 5 hours later it would likely be perfectly fine.
I think the final answer to your question comes down to your own personal risk tolerance and the conditions above. If you brew in luke-warm water or for a very brief time and then leave the bags out at room temperature you are just asking for trouble and eventually you may hit the loaded chamber in your own personal Russian roulette game.
For empiric answers, take your particular brewing temperature and time and compare it to the USDA tables for pasteurization. Then, look up the growth curves for the major pathogens at your storage temperature and figure out how many would likely be present after 5 hours (20 generations at 15 minutes per generation or 2^20 times more bacteria than viable after the brewing event at the end of the storage interval).