JAVASCRIPT

Error: Node Sass version 5.0.0 is incompatible with ^4.0.0.

with npm =>
1.npm uninstall node-sass
2.npm install node-sass@4.14.1
with yarn => 
1.yarn remove node-sass
2.yarn remove node-sass@4.14.1

Error: Node Sass version 5.0.0 is incompatible with ^4.0.0.

with npm =>
1. npm uninstall node-sass
2. npm install node-sass@4.14.1
with yarn => 
1. yarn remove node-sass
2. yarn add node-sass@4.14.1

// ^ Update to MR J's post

node sass version 5.0.0 is incompatible with ^4.0.0

with npm =>
1.npm uninstall node-sass
2.npm install node-sass@4.14.1
with yarn => 
1.yarn remove node-sass
2.yarn add node-sass@4.14.1

Node Sass version 5.0.0 is incompatible with ^4.0.0.

    npm uninstall node-sass
    npm install node-sass@4.14.1

Or, if using yarn (default in newer CRA versions)

    yarn remove node-sass
    yarn add node-sass@4.14.1

Node Sass version 6.0.0 is incompatible with ^4.0.0 || ^5.0.0

//this is modifed solution from  Mr J solution 
with npm =>
1.npm uninstall node-sass
2.npm install node-sass@4.14.1
with yarn => 
1.yarn remove node-sass
2.yarn add node-sass@4.14.1

Error: Node Sass version 5.0.0 is incompatible with ^4.0

npm uninstall node-sass
npm install node-sass@4.14.1

Or, if using yarn (default in newer CRA versions)

yarn remove node-sass
yarn add node-sass@4.14.1

Error: Node Sass version 5.0.0 is incompatible with ^4.0.0.

$ npm uninstall node-sass
$ npm install node-sass@4.14.1

# Or, if using yarn (default in newer CRA versions)

$ yarn remove node-sass
$ yarn add node-sass@4.14.1

Error: Node Sass version 5.0.0 is incompatible with ^4.0.0.

Solution
1 Uninstall node-sass
npm uninstall node-sass

2  use sass by:
npm install -g sass
npm install --save-dev sass

Error: Node Sass version 7.0.1 is incompatible with ^4.0.0.

#Don't use node-sass anymore
#node-sass is deprecated. Instead use sass.
npm uninstall node-sass

npm install sass

Node Sass version 7.0.0 is incompatible with ^4.0.0

npm uninstall node-sass
npm install node-sass
change the "react-scripts": "4.0.0" into "react-scripts": "4.0.3" in package.json and save
npm install
npm start

or, using yarn -

yarn remove node-sass
yarn add --dev node-sass
as above
yarn install
yarn start

Error: Node Sass version 5.0.0 is incompatible with ^4.0.0

All Possible Solution added Here 

https://exerror.com/error-node-sass-version-5-0-0-is-incompatible-with-4-0-0/