I strongly suggest that you consult with an attorney to review all of the terms of that oil and gas lease before you sign it. However, they are not trying to trick you here. Oil and gas leases have what is known as a "primary term", and if someone tells you it is a 3 year lease or a 5 year lease, this is what they are referring to. It means that within the primary term, 5 years in your case, they have the exclusive right to explore for and drill for oil and gas on your land. They typically pay a cash bonus up front, and unless they find oil/gas within the primary term, they will not pay you anything else under the lease.
If, at the end of 5 years, they have not started producing oil and gas from your property or pooled your property with other properties which are producing, then the lease expires.
For Barnett Shale leases, the most common primary term is 3 years, with an option to extend an additional 2 years by paying another bonus, however, 5 year leases are not unusual.
All (or almost all) oil and gas leases have the exact same language about "as long thereafter as oil, gas..."
This is because many oil and gas wells will produce for several years, and if a company is going to spend a lot of money to drill a well, they want to have the right to produce from that well as long as they can. This is why the ROYALTY is so important to you. The royalty rate is how much they pay you for the oil and gas that they produce from your land. In the grand scheme of things, the bonus that they pay up front is small potatoes compared to the amount of royalty you will receive over time if they successfully drill a well. Some wells will produce for 10, 20 even 50 years. You will get a check in the mail every month that the well continues to produce in paying quantities.
Oil and gas landowners do not get rich by entering into new leases every few years, they get rich (if they ever do) by entering into one good lease and having good wells drilled on it.
I hope that this helps. There are a lot of factors that are involved in the negotiation of an oil and gas lease, and it is unlikely that you will get the help you need from internet research alone. Find a good oil and gas lawyer in your area and have them read the lease and advise you of any terms that are troubling. It is very rare that oil and gas lease offers are "take it or leave it" propositions, so a little advice and negotiating by a good lawyer can save you a lot of money in the long run.