Relating back to the topic, I think the first step is addressing your player's concerns. There have been a lot of posts suggesting to focus more on roleplaying, or rather, that 5E is at its best when not focused wholly on combat, but I suspect that that advice will be of little use to you if your players want interesting tactical challenges. Not everyone is at the table to tell the story of Tom the righteous knight and his struggle with a dark past, some are there to play Tom the warlord who conquers the battlefield with tactical brilliance (interesting how 4E edition has a Warlord class and 5E does not. Not trying to revive any old debates here, but I think it's perhaps amusingly meaningful).
My advice to you? Keep running the system and try to get a feel for it. Once you feel you understand it well enough, start pushing its boundaries. If it seems like it's going to break, put some patches on it. Every table plays their own version of DnD. Maybe DnD 5E isn't the right system for you, maybe it is, but if you want to stick with it, chances are you can make something out of it that you and your players like. After playing 4th edition for about a year, I steadily became more and more confident in my ability to create custom monsters and challenges within the context of the rules in order to challenge the party. There were successes, failures, and varying degrees of both.
I'm not there yet in 5th edition (been playing a while, DMing a much shorter period), but I see enough hints of 4th edition design philosophy to be confident that there exists the possibility for some tactical depth to exist within the rules. It may take some doing, but I think the ability to provide a tactical challenge to your players is there. It will take small, simple steps, like ditching Theater of the Mind (which impedes your ability to provide any interesting tactical challenge, but is decent for running more narrative-focused combat) in favor of a proper grid, and larger, more ambitious steps, like home-brewing vicious boss monsters.
A short while ago I was in a party comprised of four characters of varying levels between 3 and 5, that fought a monstrosity homebrewed by the DM--a gigantic shambling mass of blood that dissolved into imps, literally throwing imps at us each turn. As it split into imps, its HP went down, disseminating into the imps. By the time it fully dissolved, it had made somewhere between 18 and 22ish imps. Going purely by EXP guidelines, that's a ridiculously deadly encounter for characters of that level, but because they came in waves and we wore down the creature with attacks along the way, and had good use of spells like Spirit Guardians, Hypnotic Pattern, Sleep, and Spiritual Weapon, along with battle-oriented characters capable of holding a melee line and slicing through things, we were able to overcome it, though not without difficulty--one player died, and another was briefly unconscious. Thankfully Revivify got the player back on their feet afterward, but it almost went very badly (if the cleric had been the one that died instead, that wouldn't have been an option, and it was about 1 round from that point when things were resolved).
Where I'm going with this is I have a lot of hope for 5E, and I think you can make some interesting combats with it, while thankfully avoiding some key issues that put me off of 4E and 3E (lots of small bonuses stacking making bookkeeping a hassle, buff-stacking, hilarious levels of class imbalance in 3rd).