PoD (Print on Demand) is becoming more common and that will affect the number of people buying the old out of print RPG books. As example, WoTC on drivethrurpg.com is offering a slew of old AD&D stuff as PoD. Here's a youtube review of one with a side-by-side comparison.
While that will not affect the true collectors, it will cut out all the people that want the books just to use them.
As for price, it's basically what the market will bear. There are no universal firm listings like with comic books but some folks try to do that, see Rulebooks Index. You can get better ideas on price by looking at past and current prices on sites like ebay or amazon. Both sites have lots of second hand books for sell.
I'll list a few for AD&D but you should Google for whatever games you have.
Or you can look at this other question, it had some good information and links to resources.
As far as I can tell, the books don't explicitly state that they are for 5th edition.
However, there's a phrase on the back that says:
When you're ready for even more, expand your adventures with the fifth edition other core rulebook #1 and other core rulebook #2.
That's at least an indirect hint that the book is for 5e.
Volo's Guide To Monsters (and probably also the other non-core-rulebooks, but I don't have those atm) states on the back cover:
For use with the fifth edition Player's Handbook, Monster Manual, and Dungeon Master's Guide.
There is also one tiny, indirect hint in the Dungeon Master's Guide, p. 11, that indicates that the book is for an edition past 4e (which, currently, only leaves 5e afaik):
The pantheon of the Dawn War is an example of a
pantheon assembled from mostly preexisting elements
to suit the needs of a particular campaign. This is
the default pantheon in the fourth edition Player's
Handbook (2008). The pantheon is summarized in the
Dawn War Deities table. [...]
I couldn't find anything else in the PHB or MM.
On a side note, I recommend checking out this question: How do I know which edition of Dungeons and Dragons (D&D) the books I'm looking at are for?.
It's not an obvious indication since you need to know which logo equals which edition, but if you find a random D&D book that doesn't specify its edition, you can compare the logos.
Best Answer
Those books were licensed reprints done by a now-defunct third party company, Twenty-First Century Games, sometime in the late 1990s or early 2000s after TSR had been bought by Wizards of the Coast but before WotC began publishing their 3rd edition of D&D. They were created specifically for the collector's market, and it appears that their value has gone up since then. They are long since out of print.
Depending on the exact books and how many you have, these are worth a bit of pocket change compared to their original retail value. Noble Knight, an online retailer specialising in out-of-print roleplaying and wargaming products, has a section for Twenty-First Century Games's AD&D reprints that lists the miniature Dungeon Master's Guide at US$50, among others. Currently, eBay is listing a sale of the miniature Wilderness Survival Guide at 51 Euro (~US$64) or-best-offer (plus shipping from Italy), but that's probably not an accurate valuation of the book, as Noble Knight is selling the same for just US$15 plus shipping.
The value of your books individually is probably somewhere in there. Depending on the exact composition of the collection, it may also have additional value as a set to someone.
And therein lies the difficulty: you won't find anywhere to unload these for full value without a bit of work, and some skill in selling collector's items. The easy route would be to sell them to a reseller like Noble Knight, which will give you some fraction of their value but is relatively effortless; the hard route would be eBaying them or similar, as a set or individually, but only you can factor how much your time and the headache of shipping is worth to you.
I don't think this has given you a full, stand-alone answer that you can skip off to the bank with; but I hope it has given you the means and knowledge to move forward in the direction that most suits your resources and goals.