"Do you start the course on April fifth?"
Translation:¿Empiezas el curso el cinco de abril?
In Spanish, the article "el" substitutes for the word "en" when talking about days of the week. I don't know why -- "them's the rules." Try not to get too hung up on the "why" behind every rule that doesn't seem to make sense to you. (Why is the "Ace" both "1" and higher than a King in some card games? Doesn't matter -- just learn the rules if you want to play the game.) I've found it to be counterproductive at this stage of the game. As we learn more, we internalize the rules (much as we do when we get good at a new card game), and then we can just use them without thinking about them each time.
So: I go to the store on Wednesday = Voy a la tienda el miércoles.
Bonus: I go to the store on WednesdayS = Voy a la tienda LOS miércoles.
According to https://www.collinsdictionary.com/dictionary/english-spanish/begin and https://www.spanishdict.com/translate/to%20begin, both "empezar" and "comenzar" are translations for "to begin." In both sites, "empezar" is listed first, but DUO is usually not THAT picky.
So I'm not sure why Duo did not accept "comienzas" in this sentence.
Here's a quick and good article on dates in Spanish. Unlike in English, ordinal numbers (e.g., "fifth") are not used. https://spanish.kwiziq.com/revision/grammar/expressing-dates-in-spanish
And you don't use "los" with the date. The reason you use "las" when telling time is one is really counting hours: "Son las cinco de la mañana." (It's five [hours] in the morning.) Of course, when it's one o'clock, one uses "la una."
BTW, thanks Emerald; here's a belated lingot.
See this article that explains that "empezar" and "comenzar" require the "a" before being used with an INFINITIVE (much like "ir" does to form the "going to" construction): https://spanish.kwiziq.com/revision/grammar/empezarcomenzar-a-infinitivo-to-beginstart-doing-something
Ella empieza a estudiar. = She starts/begins studying.
Él comienza a bailar. = He starts/begins dancing.
Voy a hablar con mi madre. = I'm going to talk with my mother.
Ella empieza su trabajo nuevo mañana. = She begins her new job tomorrow.
Él comienza la excursión esta tarde. = He begins the hike/excursion this afternoon.