Final answer:
The correct form of the verb 'to work' for the situation described is "I have been working." This uses the present perfect continuous tense, which is suitable for describing actions that started in the past and are still ongoing.
Step-by-step explanation:
The student's question is asking to determine the correct form of the verb 'to work' to describe a situation where the activity has been ongoing over the past five weeks and is still continuing. When expressing actions that began in the past and continue to the present, we use the present perfect continuous tense. This tense is formed using the present tense of the auxiliary verb 'to have' (have/has) with the past participle of 'to be' (been) plus the '-ing' form of the main verb.
In this case, the subject is 'I,' so the correct form of 'to have' is 'have.' The correct sentence is thus "I have been working for five weeks without rest." It indicates that the action started five weeks ago and is still in progress at the time of speaking.