Как использовать @RestTemplateClient с JUnit 5?

Я проверил ваш случай с последней весной загрузки 2.1.7 и junit 5, и все работает нормально. Пожалуйста попробуйте :

Pom.xml:

<?xml version="1.0" encoding="UTF-8"?>
<project xmlns="http://maven.apache.org/POM/4.0.0"
         xmlns:xsi="http://www.w3.org/2001/XMLSchema-instance"
         xsi:schemaLocation="http://maven.apache.org/POM/4.0.0 http://maven.apache.org/xsd/maven-4.0.0.xsd">
    <modelVersion>4.0.0</modelVersion>

    <groupId>com.zpavel</groupId>
    <artifactId>test</artifactId>
    <version>1.0-SNAPSHOT</version>

    <parent>
        <groupId>org.springframework.boot</groupId>
        <artifactId>spring-boot-starter-parent</artifactId>
        <version>2.1.7.RELEASE</version>
        <relativePath/>
    </parent>

    <dependencies>
        <dependency>
            <groupId>org.springframework.boot</groupId>
            <artifactId>spring-boot-starter-data-jpa</artifactId>
        </dependency>
        <dependency>
            <groupId>org.springframework.boot</groupId>
            <artifactId>spring-boot-starter-data-rest</artifactId>
        </dependency>
        <dependency>
            <groupId>org.mariadb.jdbc</groupId>
            <artifactId>mariadb-java-client</artifactId>
            <version>2.4.3</version>
        </dependency>
        <dependency>
            <groupId>com.h2database</groupId>
            <artifactId>h2</artifactId>
            <scope>runtime</scope>
            <version>1.4.199</version>
        </dependency>
        <dependency>
            <groupId>org.projectlombok</groupId>
            <artifactId>lombok</artifactId>
            <version>1.18.8</version>
        </dependency>
        <dependency>
            <groupId>org.springframework.boot</groupId>
            <artifactId>spring-boot-starter-test</artifactId>
            <exclusions>
                <exclusion>
                    <groupId>junit</groupId>
                    <artifactId>junit</artifactId>
                </exclusion>
            </exclusions>
            <scope>test</scope>
        </dependency>
        <dependency>
            <groupId>org.junit.jupiter</groupId>
            <artifactId>junit-jupiter-engine</artifactId>
            <scope>test</scope>
        </dependency>
    </dependencies>
</project>

Application.properties (я использовал базу данных h2 в памяти):

spring.datasource.url=jdbc:h2:mem:testdb
spring.datasource.driverClassName=org.h2.Driver
spring.datasource.username=sa
spring.datasource.password=password
spring.jpa.database-platform=org.hibernate.dialect.H2Dialect

FooService.java:

@Service
public class FooService {

    private final RestTemplate restTemplate;

    public FooService(RestTemplateBuilder restTemplateBuilder) {
        this.restTemplate = restTemplateBuilder.build();
    }

    public String getIndex() {
        String result = restTemplate.getForObject("http://localhost:8080", String.class);
        System.out.println("index: " + result);
        return result;
    }
}

FooServiceTest.java:

@RestClientTest(FooService.class)
public class FooServiceTest {

    @Autowired
    private FooService service;

    @Autowired
    private MockRestServiceServer server;

    @Test
    public void testIndex() throws Exception {
        this.server.expect(requestTo("http://localhost:8080")).andRespond(withSuccess("hello", MediaType.TEXT_PLAIN));
        String greeting = this.service.getIndex();
        assertEquals(greeting, "hello");
    }
}