Due to being a slime, you are immune to Suffocation, Blinded, and Prone.

Due to being a slime you are resistant to Acid and Poison as well as Bludgeoning, Piercing, and Slashing from Nonmagical Weapons

A Shape unlimited... Nearly.

Squeezing

You can move through a space as little as your core, which is roughly the size of a human skull. If any equipment you’re holding or carrying is larger than the space you are attempting to pass through, it gets left behind.

The Cost of Formlessness

Due to your formless body, you are unable to wear armor or most clothing. This does not prevent the use of shields or some magic items at the discretion of the DM.

Falling into a large body (like an ocean or lake) of water immediately begins to dilute your fluid body, upon entering water take (8 x The amount of you submerged in fourths*) x Proficiency modifier straight damage, Begin rolling death saves to prevent yourself from diluting. 

*IE if its up to your knees take (8 x 1/4) x Proficiency modifier.

Physical Mimicry

Cored Oozes have the habit of morphing themselves to match those they interact with, the copy isn't passable by any means, it does not function as alter or disguise self, but it does tend to unsettle people. 

Acid Splash

You concentrate some of the acidic properties of yourself into a miniature pseudopod which you fire off towards your target, allowing you inherent access to acid splash once per long rest. 

Supported Form

An Ooze's form is incredibly fluid and as such it is difficult to retain some forms, including humanoid ones, to help with this Cored Oozes can use things like bones to help give them a shape, things used in this way are corroded as normal.

Engulf.

Rather than grappling as normal, you engulf them within yourself. When making a grappling check you can choose to use your Constitution in place of your Strength. Additionally, as an action you can attempt to engulf an object or creature of your size or smaller within 5 ft. of yourself. A creature must succeed a Dexterity saving throw or be grappled by you. A creature grappled this way is partially engulfed in your body and is restrained for the duration of the grapple. You can have one creature or object grappled this way at a time.

DC = 9 + your proficiency modifier + your Constitution modifier

You have 10 feet of Blindsight and 60 feet of Tremorsense.

Due to your lack of normal sight you are unable to read, notice patterns on a surface, see color, or write. You are also unable to see things beyond 10 feet of you that are not moving.

However, you are immune to visual illusions.

The magical core alters the acidic digestive properties of an Ooze as a side effect of the intelligence it provides, causing the cells to always be in a state of digestion. The items touching you dissolve given enough time, including your equipment. An Ooze can choose to concentrate on preventing themselves from dissolving the things touching them, this concentration can be broken as normal, and can additionally be broken by using other abilities outlined in the Cored Ooze race, excluding telepathy and the sensing of an environment.

Digestion Times

The following times assume you are in consistent contact with a particular object. Times will likely vary beyond the scope of these numbers.

Liquids in small amounts are absorbed.

Paper dissolves in 1 minute.

Cloth and rope dissolve in 5 minutes.

Food, skin, muscles, plants and other similar organic things dissolve in 10 minutes. This counts as beneficial sustenance for purposes of feeding yourself in high enough amounts at the call of the DM.

wood dissolves in 1 hour.

1 inch of Bone dissolves in 2 days. This counts as beneficial sustenance for purposes of feeding yourself in high enough amounts at the call of the DM.

2 inches of iron or steel dissolves in 3 days.

Stone, crystal, glass, mithril, and adamantine do not dissolve.

Magical items do not dissolve.

Ice melts at a significantly increased pace when in contact with you regardless of your temperature.

You can create up to 2 pseudopods at a time, these are prehensile, they function as your arms, they can originate at any point of your body.

Your unarmed attacks deal 1d4 bludgeoning and acid damage. The strength of the acid grows as you become stronger, moving up a single damage dice every 5 levels, starting at 1d4. 

IE 1d4 to 1d6 to 1d8 and so on

The magical core within an Ooze, explained at its most basic, enchants the cells around it, the enchantment allows for the Ooze to communicate with those around it in a language both understand.

You can telepathically communicate with up to 10 creatures you can sense via blindsight or tremorsense.

The magical core within you has endowed your cells with intelligence, as a reaction when you would be reduced to 0 hp by lightning or slashing damage and still have at least 1 hit dice remaining, you may choose to split yourself into a number of Oozes equal to your remaining hit dice. each of these Oozes has a speed of 10 ft and hit points equal to one hit dice plus con mod. at the end of a long rest any remaining oozes reform together into your body. New Oozes are one size smaller than the original ooze.

As a side effect of sentience, you require at least 4 hours of rest for your surrogate mind each day. Resting in this way grants the same benefit that a human gains from 8 hours of sleep. You cannot be woken during this time.

There are currently no known instances of a Ooze dying due to age. However, the oldest documented lifespan of a Ooze currently is 650 years, though it was slaughtered shortly after discovery.

Your Ooze however is unique, as it has been allowed intelligence through magic imbued within a core of some kind, so while death might not be inevitable, there's a chance consciousness is finite, as eventually you might corrode your own core.

Your Constitution and Strength score increases by 2. 

Your intelligence decreases by 3.

Oozes tend to be chaotic neutral, more often than not they're only driven with the desire to consume.

Oozes are around 4 to 5 feet tall and can weigh anywhere between 80 and 150 pounds. Your size is Medium.

Your walking speed is 20 feet. You cannot move faster.

You have the effect of Spider Climb at all times affecting only you.

You are completely unable to swim.

You speak common, but only through telepathy.