How do you pronounce "fifths"?

The Big Book of Beastly Mispronunciations says:

fifth FIFTH or FITH
If you can pronounce the second f, good for you. But there's nothing slovenly or improper about dropping it and rhyming fifth with pith and myth.

Disclaimer: I do not agree with some of their verdicts of "beastly": the entry goes on to say It is beastly, however, to drop the h and say FIFT or drop the th and say FIF.

Regarding the plural, fifths: the above excerpt applies pretty well here too. /fifθs/ is possible for many native speakers, and /fiθs/ is quite acceptable.

Howjsay.com has both pronunciations in audio (BrE), and forvo.com only has /fifθs/ (in AmE). Forvo also has eight pronunciations of fifth in various contexts (e.g. Fifth Avenue). Check them out if you want to hear them spoken.

English has some prodigious consonant clusters - look at angsts /æŋksts/, twelfths /twɛlfθs/, sixths /sɪksθs/ - and, yes, an overwhelming proportion of its adult speakers can pronounce them all in careful speech. However, in rapid speech they are reduced.

Some common consonant reductions routinely take place. For example, American dialects tend to remove /j/ from initial clusters, and Caribbean and African-American Vernacular English tend to have more cluster reductions than some other varieties, including θ -> t, f, Ø.

EDIT: So to take your example of 'fifths': you'll find variants that range from [fɪfθs] and [fɪθsː] and [fɪfsː] (all fairly standard) to [fɪfts] [fɪsː] [fɪts] (less standard and perhaps stigmatized).

Clothes is not a plural of a noun clothe. It is an antique plural of the word cloth.

clothes /kloʊz/ means one's garments. He is wearing clothes.
clothes /kloʊðz/ is the 3rd person singular of the verb 'to clothe'. The mother clothes her child.

Mouths is usually pronounced either [maʊθz] or [maʊðz], not [maʊz] in the standard language.

Native AmE speakers routinely pronounce 'fifths' as

[fifs]

or

[fiθs]

(I had thought the latter less common, but now I'm not sure). It is usually only actors or newscasters who will attempt to articulate the entire sequence [fifθs]. See the question about other difficult clusters like -sps.