There are different ways to use Mockito - I'll go through them one by one.

Manually

Creating mocks manually with Mockito::mock works regardless of the JUnit version (or test framework for that matter).

Annotation Based

Using the @Mock-annotation and the corresponding call to MockitoAnnotations::initMocks to create mocks works regardless of the JUnit version (or test framework for that matter but Java 9 could interfere here, depending on whether the test code ends up in a module or not).

Mockito Extension

JUnit 5 has a powerful extension model and Mockito recently published one under the group / artifact ID org.mockito : mockito-junit-jupiter.

You can apply the extension by adding @ExtendWith(MockitoExtension.class) to the test class and annotating mocked fields with @Mock. From MockitoExtension's JavaDoc:

@ExtendWith(MockitoExtension.class)
public class ExampleTest {

    @Mock
    private List list;

    @Test
    public void shouldDoSomething() {
        list.add(100);
    }

}

The MockitoExtension documentation describes other ways to instantiate mocks, for example with constructor injection (if you rpefer final fields in test classes).

No Rules, No Runners

JUnit 4 rules and runners don't work in JUnit 5, so the MockitoRule and the Mockito runner can not be used.