What part of speech are the words 'their' and 'out' in this sentence? "These cost cutting measures work to their disadvantage'. 'Five reasons...

"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!)

Good luck!