I'm not a lawyer, either, and would agree with the suggestion that if you want to proceed, you should consult a firearms-savvy Texas lawyer. However, I'm pretty sure that, as you were told, once 5 years has elapsed following your final completion of sentence (including any probation / parole / supervised time period), and you have not re-offended, then you are allowed to possess a long gun in your home. My recollection is that it is long gun only (i.e., not applicable to handguns), and it is in your home only (i.e., hunting is right out - unless your house is situated such that you can "hunt" from your back porch). I believe, but am not certain, that this is found in Chapter 46 of the Texas Penal code, maybe 46.02; you can google that and see if it's there.
As far as someone's comment about how you can be disabled under Federal law from "receiving" a firearm yet still be enabled under State law to possess a long gun in your home, I believe it gets to states' rights and the deference that Fed law generally shows to State laws. Like, in Louisiana, once you complete your sentence entirely for your FIRST felony conviction, your record is expunged upon your release (an ATF attorney told me this was the case in about 1994). I believe in your case you would be unable to pass an NICS background check, so you would need to buy a long gun from a relative / friend.
Again, seek a lawyer's advice, I may be wrong, as my info is somewhat dated since I haven't checked up on this stuff for several years.