I'm having a hard time challenging my party because my wizard has been doing an amazing job stun locking enemies with Tasha's Heideous Laughter. Boss fights have been trivialized. The party is level 5, and because of mistakes I've made in the form of magic items, the Wizard's Spell DC is 16.

I want to challenge the party but not by fiat or unfair bullshit.

Well I am not sure what sort of answer you expect that you would not consider "fiat" or "unfair bullshit." Literally anything you do as a DM to counter an ability you know the players have could possibly fall under the category of "DM Fiat." 

I can see the following possible ways of dealing with this:

• Enemies with INT < 4 - these are immune to the spell according to the text. A large number of beasts fit this category.
• Enemies with very high WIS - these will be more likely to save vs. the DC 16. You're going to need WIS in the 18+ range for this and even then... they will fail. The effectiveness of high WIS will be random.
• Tactics. It's a concentration spell. Have the target's buddy go after the caster and try to disrupt his concentration.
• Dilution effect. Hit them with lots of weak enemies rather than one big bad -- the spell can only be an "I win" button if taking one guy out of the battle is a big deal. If the level 5 party is fighting, say, 10 normal orcs, taking one out with the laughter isn't going to be as effective as taking out the Orc Chief in a room with him and just 2 minions would be.
• Counterspell. At this point they should be getting to where they are fighting enemies whose mage allies can last 3rd level spells. Give the enemy mages counterspell and have them block it. Tasha's is level 1 -- counterspell will auto-succeed.

Now... I dunno if you consider any of these "DM Fiat" or "bullshit," but those all are, IMO, legitimate things that could come into play (not all at once!) to challenge the party. Remember, it won't be any fun for the players (or it shouldn't be!) if they just have an I win! button all the time anyway.

Are you remembering to give the target saves with advantage each time it takes damage?

Throw more encounters at them in a day. Wizard at that level can cast it four times max. If they are memorizing it four times, maybe throw some situations at them where some utility spells would come up (or start making them wish they had shield prepared) and make them rethink their strategy of always having tasha ready. 

Several good ideas already:

• more encounters per day
• enemies that target the wizard
• "boss monsters" revealing themselves in round 2 or 3 of the fight
• "action oriented monsters"  that can perform certain actions NOT on their turn (even out action economy)
• enemies with resistances/saves
• If the party talks about their exploits at an inn,  unscupulous information vendors may sell tactical information to "concerned parties" aka bad guys
• terrain and line of sight considerations
• tactical positioning (monsters getting to the back line)

As your characters increase in level and power you're going to end up with a lot more of these situations and encounter balancing becomes more challenging.  That's part of the fun! 

Quote from Whiskeyjack8044 >>

I'm having a hard time challenging my party because my wizard has been doing an amazing job stun locking enemies with Tasha's Heideous Laughter. Boss fights have been trivialized. The party is level 5, and because of mistakes I've made in the form of magic items, the Wizard's Spell DC is 16.

It might help to destroy the magic items (what magic items boost spell save DC anyway?) but a vanilla wizard probably has save DC 15 so it won't help much. You can also use bosses with Int 4 or lower, proficiency with wisdom saves, magic resistance, bosses that can't be seen (other than invisible bosses, any form of heavy concealment; a lot of spells are negated by Fog Cloud). Also, remember that Hideous Laughter has a check every time the victim takes damage, with advantage. Unfortunately, there aren't a lot of bosses with legendary resistance at the CR 8-10 you'd want for a challenging solo at level 5, but something like a Glabrezu (Hard fight for 5 PCs, Deadly for 4) is not going to be usefully vulnerable to Hideous Laughter.

Have a magic user cast silence in a surprise round or blind the caster with some other spell.  Laughter has a verbal component and effects a target the caster can see.  Alternately, have the caster snared in a trap or grappled in a way they cannot move their arms since the spell has a somatic component.  I like silence as a counter.  It mostly takes spell casters out because so many spells have a verbal component.

i just checked and hideous laughter has range of 30 ft while silence is 120, so you don’t even need surprise.

I think more encounters per day is an important one that has been mentioned a couple of times, but I plum forgot about.

The other thing to consider, if we're talking about someone preparing spells, is that Tasha's needs to be prepared for such a caster (i.e., the wizard mentioned). Well, OK, if you prepare that, what other spells are you not preparing that day? Let's say he has +4 INT and is level 5, that's 9 spells he can prepare of 1st through 3rd level. I think it's time he encountered some situations in which Tasha's would not help him, but other spells he isn't preparing so he can prepare Tasha's would have -- spells like Featherfall, or Charm Person, or Arcane Lock, or Disguise Self, or Detect Magic, or... the list goes on. Tasha's isn't going to help him when he needs one of those spells. If he sees enough cases in which having prepped Tasha's leaves him wanting another spell, maybe he'll prep something else for a change.