I support DL 100% here with their translation: I try to sleep. INTENTAR is much better translated as to try than to intend. May even be considered a false cognate since the Spanish for to intend is best translated as tener la intención. "Tengo la intention de estudiar idiomas en la universidad." (Harper Collins Beginners Spanish Dictionary, 2001). INTENTAR is used often. We should master it.
(Late reply is late)
Grammatically, "to sleep" and "sleeping" are not interchangeable. The first is the infinitive form of the verb, as is dormir. The second is the gerund -- the Spanish equivalent would be durmiendo. "Try" in English can take either type. I don't know if "intentar" in Spanish could be done with a gerund (intento durmiendo), but regardless, "sleeping" isn't a direct translation of "dormir".
I think you may have a good case for your translation. According to my grammar book, "When the -ing form is the object of the verb -and- the same subject performs both actions, use an infinitive or a noun."
In that case, I try sleeping = Intento dormir.
p.s. How are you liking the reverse course?
The -o ending is first person present: como is I eat, bebo is I drink, intento is I try. Don't get it confused with -ó, which is third person past (preterite): Intentó dormir is "he/she tried to sleep". Intento is accented on the next-to-last syllable (inTENto), whereas intentó is accented on the last (intenTO).
First person past would be intenté (which itself shouldn't be confused with intente, which is a different verb ending).
If you're confused because "I try to sleep" doesn't sound like a thing said in English, think of the two following conversations:
"Don't call me between 9pm and 10pm." "Why, what happens then?" "That's when I fall asleep. Well... I try to sleep. If I'm not asleep by 10, I will be up for another two hours at least."
"Can you keep the noise down? I'm trying to sleep!"
(The present tense in Spanish is used both for the simple present, like "I try", and the present continuous, "I am trying".)