One of the ways to run JUnit 4 and JUnit 5 test cases side-by-side is to use JUnit Vintage engine:
<dependencies>
<dependency>
<groupId>junit</groupId>
<artifactId>junit</artifactId>
<version>4.13.1</version>
<scope>test</scope>
</dependency>
<dependency>
<groupId>org.junit.jupiter</groupId>
<artifactId>junit-jupiter</artifactId>
<version>5.7.0</version>
<scope>test</scope>
</dependency>
...
</dependencies>
<build>
<plugins>
<plugin>
<groupId>org.apache.maven.plugins</groupId>
<artifactId>maven-surefire-plugin</artifactId>
<version>3.0.0-M5</version>
<dependencies>
<dependency>
<groupId>org.junit.vintage</groupId>
<artifactId>junit-vintage-engine</artifactId>
<version>5.7.0</version>
</dependency>
</dependencies>
</plugin>
...
</plugins>
</build>