"These cost-cutting measures work to their advantage."
"These" is a pronoun acting as an adjective telling us what measures.
"cost-cutting" is two words acting as one (hence the hyphen) telling us what kind of measures we have. It is an adjective.
"measures" is a noun. It is the subject of the sentence.
"to" is a preposition, the object of that preposition is "advantage". Therefore, "advantage" is a noun.
"their" is a pronoun. It is always a plural possessive pronoun.
"Five reasons stand out."
"Five" is an adjective telling you about "reasons".
"reasons" is a noun and the subject of the sentence.
"stand" is the verb.
"out" is a noun. It is acting as the direct object in this sentence. To find the direct object, find the subject and verb and ask the question "who or what". If you have an answer, you have a direct object. "Reasons + stand + who/what" = "out".
Remember that different words can function as different parts of speech depending on context, so you must always ask yourself, "What is this word telling me more about in the sentence?" It is easier to determine parts of speech once you figure out the subject and the verb of the sentence. Everything else is extra and is telling you something more about the subject or verb, usually.
Adjectives--tell about a noun or pronoun
Adverbs--tell about a verb, adjective, or other adverb. Usually, but not always ends in "-ly".
Pronouns--take the place of nouns. There are several types of pronouns. You should brush up on these.
Nouns--person, place, thing or idea.
Verbs--action word or state of being word (am, is, are, was, were, be, being, been)
Prepositions--relate words in the sentence. (My house is ON the hill NEXT TO the store, BEHIND the woods, and IN FRONT OF the school).
Conjunctions--connect words, phrases, and clauses
Interjections--show emotion (Shoot! Oh, no! Duck!)