Texas' statutes on this are pretty confusing. We've got three different sections that can apply to disposing of a seized firearm and the results can all be different. The first thing I'd do is look up the criminal case records. If by HPD you do mean its a Harris Co. criminal case than all of their records are available online. See if there is any order saying what happened with the firearm. Options include returning the firearm to the defendant, ordering a forfeiture of the gun to the agency or DA's office, or destruction of the firearm.
Five years after a dismissal it is very likely that the gun was either given back to the defendant or forfeited to the State as abandoned property, meaning it was either sold or destroyed. But that's not a given. Agencies of all sizes are notorious for getting backlogs on their evidence. They do audits periodically and either return or get destruction orders on items seized in old cases. Its entirely possible your gun is still in an evidence locker. You can try calling the police agency and asking to speak to someone in the property room to see if they still have the gun. I've seen guns still sitting on evidence room shelves 20 years later. It all comes down to how good the property clerks are and whether your case/item is the one that slipped through the cracks.
With all that said, you likely missed the boat on this. Firearms are generally not traceable unless you report it stolen. The only record of a firearm in Texas is the initial purchase but neither the agency nor the DA's office is required to go notify the original purchaser that they have a gun in evidence that might belong to them. Unless they have some specific reason to suspect that the gun belongs to someone else, they will treat it as the defendant's gun. That means if he/she is convicted the gun is destroyed. If he/she is not convicted then they can have the gun back. If he/she is not convicted but never asks for the gun back, they destroy it. As the actual owner of the gun you are required to step in and claim ownership while the case is still pending or shortly after its disposed of, (approximately 121 days.)