Does the Divine Health feature negate the main effect of this spell? (Choosing the effect)

can any one mention the huge elephant in the room forget slimy doom  do flesh rott have fun doing like 50 to 40 damage with a 3rd level fireball contagion is op   also the effects are really good like mindfire basicly a better confusion so yes contagion  is broken you know what is garbage tho contingency that spell is bad  so  so stay off my cast contagion divination wizard after they fail all saves turn to anchent white dragon and do way to much damage cuz flesh rott does double damage to enemies so op if your divination 

make a divination wizard cast it choose theyr roles  after words use flesh rott then cast shapechange turn into anchent white dragon and absolutely destroy them

*sigh* WHY DOES EVERYONE HATE CONTAGION IT IS OP

lyssas_faith if correct it is really good espasaly as a divination wizard with shape change

Why contagion is a solid choice

Easy way to make one hard-hitting enemy less dangerous and easier to handle for an extended time

For the creatures that are not immune, this is a concentration-free, broad debuff that's relatively easy to land because it requires an attack roll instead of an up-front saving throw.  Once you hit, the poisoned condition imposes disadvantage on all attack rolls and all ability checks.  And it's sticky: even if the creature has great CON saves or uses legendary resistances, those won't end the condition for three to five rounds, because it makes one save at the end of its turn and has to succeed three times.  Since it doesn't require concentration, enemies can't end the spell by damaging or incapacitating the caster.  If you hit, you've just tilted the combat against one big enemy.

Imposing disadvantage on all ability checks has several benefits in combat.  As Lyssas_Faith pointed out, it reduces the enemy's passive Perception by 5, making it significantly easier for your rogue to Hide.  On the flip side, it gives sneaky enemies disadvantage on their Stealth checks.  It also imposes disadvantage on Athletics and Acrobatics checks to deal with environmental obstacles and avoid being grappled or shoved.  It imposes disadvantage on their counterspell and dispel magic checks (so a creature trying to dispel contagion from itself during battle would do so with disadvantage on the roll, unless it used a 5th-level spell slot).  And it does all these things at the same time.
Lots of spells that trap or move enemies require an ability check to escape.  The best examples, because they don't allow a saving throw, are Bigby's hand (no save against Forceful Hand to shove or Grasping Hand to grapple), telekinesis, maze, ravenous void (for creatures that start in the sphere), and, if you happen to catch them swimming on the surface of water, freezing sphere. And creatures use ability checks to escape from tsunami, whirlwind, wrath of nature (Roots and Vines), entangle, web, and black tentacles if they fail a saving throw.  In the right environments there's control water (Whirlpool), transmute rock (Mud to Rock), and earthquake (Structures).  You can even get creative with immovable object.
Naturally, the same goes for items like the iron bands of Bilarro, dimensional shackles, or immovable rod.
And most illusions offer an ability check to see through them: major image, programmed illusion, illusory dragon, phantasmal force, etc.
Even wrathful smite, which can block the enemy's movement, offers a Wisdom check to end the spell, and this ensures they still have disadvantage even if the smiter is not within line of sight.

The disease is just the cherry on top 

If the combat goes on long enough and the target rolls poorly enough that the disease actually takes hold, it's a nasty effect that should accelerate their downfall in the final phase of combat.  By then you've had three to five rounds to learn the enemy's strengths and weaknesses, so you can make an informed choice about which disease would be most effective.  Even if the villain gets away, the spell makes their life harder for the next 7 days without any saves. 
Realistically, some of the enemies you'd target with contagion have access to a spell, item, or ability that cures diseases, but many don't, especially if they're on the run or they're in a low-magic setting.  Depending on their situation, it may be harder to escape or recover when they're blinded or have rotting flesh that kills their Charisma checks.  If you targeted the enemy's spellcasting ability and it tries to cast dispel magic on itself without burning at least a 5th-level spell slot, there's a good chance it fails.

Making the most of contagion

Several metamagic options can make this spell shine.  If you're a Divine Soul sorcerer or have the Metamagic Adept feat, you can cast this from 30 feet away using Distant Spell, or sneakily cast it without using any components using Subtle Spell, for 1 sorcery point either way.  It's probably worth using Seeking Spell if you miss.  If you have Quickened Spell, you can cast the spell and still have your action to Disengage or, if you hit, Dash away and risk the opportunity attack made with disadvantage.  If you have find familiar (say, from Pact of the Chain, or the Magic Initiate or Ritual Caster feats) you can send your familiar to deliver it from up to 100 feet away.

Regardless, you'll want to make sure your attack roll hits, because it hurts to cast a 5th-level spell and not get anything at all.

Most major threats have a good CON save bonus, so you have only a faint hope of making the disease take effect, but in some circumstances you may want to undercut the target's Constitution saving throws.  Maybe just to burn legendary resistances, maybe to make the poisoned condition last longer, or maybe because you really want that disease to kick in.
In that case, you could use something sticky like bestow curse or bane or polymorph.  Aside from special circumstances, it's probably not worth the investment to use silvery barbs, Portent, Chronal Shift, mind sliver, or Heightened Spell to target each saving throw separately.

Immunity

Yes, about a quarter of published monsters are immune to the poisoned condition.  Yes, it's even more common for the big threats you'd spend a 5th-level spell on: of all creatures with a CR of 8 or higher, more than a third are immune.
But you'll generally know if you're in the kind of situation where you're likely to be fighting those creatures. This spell can be quite useful if the heavy enemies you'll be facing are often going to be giants or aberrations or monstrosities or fey or common humanoids or non-green dragons or genies or vampires or celestials.  But if the heavy enemies you'll be facing are going to be fiends, non-vampire undead, non-genie elementals, yuan-ti, green dragons, and/or constructs, maybe rely on a different spell.*  (Same for creatures that are likely to have lesser restoration, heal, or a 5th-level dispel magic handy.)  If you're a cleric or druid, you can just swap the spell on a daily basis.  If you're an Undying warlock, an Oathbreaker paladin, or a Divine Soul sorcerer, just recognize that this spell is excellent against many enemies and useless against others.

But that's true of almost all spells.  A number of great spells only target certain creature types.  And many beloved spells aren't so great against enemies who have a high bonus for a particular saving throw.

* Getting around immunity (sometimes)

There is a way around immunity to the poisoned condition, but it's a bank shot that won't work most of the time.  From what I can tell, there are no monsters that are specifically written as immune to disease, though warforged characters, 3rd-level paladins, 10th-level monks, and 10th-level Circle of the Land druids are immune.  Aside from that, it's a matter of DM interpretation whether a given creature could contract a disease.  Indeed, the DMG suggests that diseases could potentially infect anything:

A disease that does more than infect a few party members is primarily a plot device. The rules help describe the effects of the disease and how it can be cured, but the specifics of how a disease works aren’t bound by a common set of rules. Diseases can affect any creature, and a given illness might or might not pass from one race or kind of creature to another. A plague might affect only constructs or undead, or sweep through a halfling neighborhood but leave other races untouched. What matters is the story you want to tell.
– Dungeon Master's Guide, chapter 8: Running the Game - Diseases

For one example, the Exandria setting features a bioweapon that was engineered to kill servants of the gods.
But contagion "induces a natural disease in its target" and a DM could easily rule that most creatures immune to poison would also be immune to most of these natural diseases—often because they lack flesh, like incorporeal undead or constructs—but other monsters may not be immune: yuan-ti and other monstrosities and humanoids, perhaps some fiends, maybe even some fleshy undead?  Maybe blinding sickness works on anything with fleshy eyes, for example?  Maybe mindfire works on anything with a brain, including various zombies?  Maybe flesh rot works on anything with muscle and sinew, and slimy doom works on anything with blood?

For those creatures that can't be poisoned but can be diseased, you could use polymorph to turn the creature into a beast that's susceptible to contagion until the disease takes hold, so that when the polymorph drops you're facing a much weaker enemy.  I'd choose a beast that's easy to hit, has a low CON save but a fair number of hit points (so nobody "kills" it before the disease takes hold), and lacks immunity to the poisoned condition, like a killer whale.

Would magic resistance give an advantage to the saving throw on this? It says it induces a natural disease but it is obviously a spell so I'm not sure

So my player casted this with meta magic (feet distance).  Used Fleshrot to double damage to my dragon making it a pretty easy kill for the party.  Vunerability to all damage.  

Could you use this with glyph of warding or contingency or similar? I feel like this isnt meant to be used during combat, but a way to debuff beforehand. 

This spell seems useless at first but when/if you consider that this spell is treated as a regular disease, it dramatically becomes more terrifying. Cast this spell on a pig or a wounded soldier and now you have a disease outbreak. This spell should be used not during combat but as part as stealth attacks before major encounters. you can take down armies with a single casting of this spell.

Slimes doom is kinda broken…

I feel like this spell is better meant for traps, long term NPC bad guys, and vengeful fey/spirits/etc.

What if someone was subjected to all these diseases at once via multiple castings?

you could give someone explosive diarrhea with this spell. just saying