Now Junit5 provides a way to assert the exceptions
You can test both general exceptions and customized exceptions 
A general exception scenario:
ExpectGeneralException.java
public void validateParameters(Integer param ) {
    if (param == null) {
        throw new NullPointerException("Null parameters are not allowed");
    }
}
ExpectGeneralExceptionTest.java
@Test
@DisplayName("Test assert NullPointerException")
void testGeneralException(TestInfo testInfo) {
    final ExpectGeneralException generalEx = new ExpectGeneralException();
     NullPointerException exception = assertThrows(NullPointerException.class, () -> {
            generalEx.validateParameters(null);
        });
    assertEquals("Null parameters are not allowed", exception.getMessage());
}
You can find a sample to test CustomException here : assert exception code sample
ExpectCustomException.java
public String constructErrorMessage(String... args) throws InvalidParameterCountException {
    if(args.length!=3) {
        throw new InvalidParameterCountException("Invalid parametercount: expected=3, passed="+args.length);
    }else {
        String message = "";
        for(String arg: args) {
            message += arg;
        }
        return message;
    }
}
ExpectCustomExceptionTest.java
@Test
@DisplayName("Test assert exception")
void testCustomException(TestInfo testInfo) {
    final ExpectCustomException expectEx = new ExpectCustomException();
     InvalidParameterCountException exception = assertThrows(InvalidParameterCountException.class, () -> {
            expectEx.constructErrorMessage("sample ","error");
        });
    assertEquals("Invalid parametercount: expected=3, passed=2", exception.getMessage());
}