In src/package.json => dependencies

• "@iobroker/adapter-react": "^2.0.22", => "@iobroker/adapter-react-v5": "^3.1.34",
• "@material-ui/core": "^4.12.3", => "@mui/material": "^5.10.9",
• "@material-ui/icons": "^4.11.2", => "@mui/icons-material": "^5.10.9",
• Add "@mui/styles": "^5.10.9",
• Add "babel-eslint": "^10.1.0",

In Source files

• All @iobroker/adapter-react/... => @iobroker/adapter-react-v5/...
• All @material-ui/icons/... => @mui/icons-material/...
• Change import { withStyles } from '@material-ui/core/styles'; => import { withStyles } from '@mui/styles';
• Change import { makeStyles } from '@mui/material/styles'; => import { makeStyles } from '@mui/styles';
• Change import withWidth from '@material-ui/core/withWidth'; => import { withWidth } from '@iobroker/adapter-react-v5';
• All @material-ui/core... => @mui/material...
• Change import { MuiThemeProvider } from '@material-ui/core/styles'; => import { ThemeProvider, StyledEngineProvider } from '@mui/material/styles';
• Change all <MuiThemeProvider theme={this.state.theme}> to <StyledEngineProvider injectFirst><ThemeProvider theme={this.state.theme}>
• Rename in styles theme.palette.type => theme.palette.mode
• Add to all TextField, Select, FormControl the property variant="standard"
• Add to all Button that do not have color property: color="grey"
• Replace by TextField the readOnly attribute (if exists) with InputProps={{readOnly: true}}
• Remove px by all theme.spacing: calc(100% - ${theme.spacing(4)}px) => calc(100% - ${theme.spacing(4)})
• Replace this.selectTab(e.target.parentNode.dataset.name, index) => this.selectTab(e.target.dataset.name, index)

If you still have questions, try to find an answer here.

Migration from adapter-react-v5@3.x to adapter-react-v5@4.x

• Look for getObjectView socket requests and replace socket.getObjectView('startKey', 'endKey', 'instance') to socket.getObjectViewSystem('instance', 'startKey', 'endKey')
• Look for calls of custom like

this.props.socket._socket.emit('getObjectView', 'system', 'custom', { startKey: '', endKey: '\u9999' }, (err, objs) => {
    (objs?.rows || []).forEach(item => console.log(item.id, item.value));
});

to

socket.getObjectViewCustom('custom', 'state', 'startKey', 'endKey').then(objects => {
    Object.keys(objects).forEach(obj => console.log(obj._id));
});

• Replace all socket.log.error('text') to socket.log('text', 'error')
• Add to App.js import { AdminConnection } from '@iobroker/adapter-react-v5'; and super(props, { Connection: AdminConnection }); if run in admin

Migration from adapter-react-v5@4.x to adapter-react-v5@5.x

• Theme is renamed to IobTheme. It is an object with classes inside. Theme is still inside and it same as mui createTheme.
• adapter-react-v5 has all types exported. So you can use import { type IobTheme, Theme } from '@iobroker/adapter-react-v5'; and const theme: IobTheme = Theme('light');
• Json-Config is now an external package and must be included as dependency separately.
• Use type Translate for t(word: string, ...args: any[]) => string
• All components for admin JsonConfig must be changed: Before adapter-react-v5@5.x:

import { ConfigGeneric, I18n } from '@iobroker/adapter-react-v5';
class JsonComponent extends ConfigGeneric {
    // ...
}

With adapter-react-v5@5.x:

import { I18n } from '@iobroker/adapter-react-v5';
import { ConfigGeneric } from '@iobroker/json-config';
class JsonComponent extends ConfigGeneric {
    // ...
}