How can I safely reuse tea?

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 bag 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).

The only "danger" I can think of would be mold growing on the damp bag, which is not really a concern over a period of five hours.

Really, though, (most) tea isn't all that expensive and it will taste better if you use a new bag.

Tea bag usually packs a very mild tea concoction unlike the regular tea granules. So for a tea bag, even a second reuse will not give you a suitable taste for your taste buds. As for experimenting I have used the teabags a second time after a gap of 10 hours (in tropical Indian climate). So far no molding came for that much time.

But if you are planning to reuse teabags for economy purpose, the best choice will be to shift from tea bag to tea leaf or tea granules or tea dust which comes cheaper as you are not going to pay the cost of the filter bags and strings, and the labour of packing each tea bag.

If you buy a decent quality tea, the leaves are edible so you should be fine using them a couple of times. Even with cheap tea bags you can stretch a few cups out of a tea bag.

Source: http://www.helium.com/items/1173756-leftover-green-tea-leaves-antibacterial-properties-within-green-tea

Plant matter + heat + moisture = potential bacterial growth in only a few hours. Don't reheat tea, unsafe and pretty gross. If you can't afford the tea you use, buy cheaper tea.

Single caveat, if it's continuously steeping and being drunk then no biggie. But if you're talking about leaving it out, don't do that.

I don't really reuse my tea bags because mainly they lose flavour quite drastically after the 2nd cup, but depending on your environment (humid/dry climate), tea bags steeped within a day and tossed out after works fine for me. Each time pouring boiling hot water.

I normally reuse loose tea leaves instead, like puerh, oolong tea leaves (even when they come in individual nylon mesh bags), for up to 2 days even and have no problems with it. I often rinse the tea leaves thrice for puerh before drinking at the first use, then across the days I add on more tea leaves to the filter, and steeped it in fresh boiling water for a couple of minutes before drinking. My mum used to boil them over the stove with the tea leaves kept from the night before.

I would place those used tea bags in the freezer until you are ready to reuse.