Hi hextejas,
Just to clarify … I’m not familiar with a store called the “Houston Mattress Store” although Texas Mattress Makers is a member of the site and are included in the Houston list here.
The only way to know for sure would be to try the combination in person but stacking a mattress that is meant to be used on its own and has separate comfort and support layers on top of another mattress isn’t likely to be nearly as effective and would also be more costly than adding a topper that is meant to add additional softness and pressure relief to an existing mattress. I would also doubt that you will need an additional 5" on top of your mattress.
If your mattress is too firm but is still in good condition and doesn’t have any soft spots (virtual impressions) or visible impressions and you just need some extra softness and pressure relief (and the foundation under the mattress is also in good condition without any soft spots or sagging as well) then a topper can certainly be an effective solution. If the mattress does have soft spots or impressions and you are hoping to use a topper to “fix” it then your results may be disappointing and at best may only provide temporary or partial results and at worst can make some issues worse. With a mattress that is 30 years old I would certainly check the condition of the mattress and the foundation carefully.
If you do decide to go in this direction then post #2 here and the topper guidelines it links to can help you use your sleeping experience as a reference point and guideline for choosing the type, thickness, and firmness for a topper that has the least possible risk and the best chance for success and also includes a link to a list of some of the better sources for toppers I’m aware of as well.
Phoenix