ごとき is basically just an outdated, stiff way of saying ような, which means "like."

It tends to show up in formal (and often flowery) written language.

Here's how we construct it:

NOUN ＋ の ＋ ごとき + NOUN
NOUN ＋ の ＋ ごとく + NOT-NOUN

Example:

地獄のごとき経験をした。
じごく　の　ごとき　けいけん　を　した。
I had an experience like hell itself.
Literally: "hell + の + ごとき + experience + を + did."

So that's:

NOUN ＋ の ＋ ごとき + NOUN
地獄＋ の ＋ ごとき + 経験
hell ＋ の ＋ ごとき + experience

→ an experience like hell

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It may help to remember that ごとき and ごとく can be used exactly like ような and ように, which we'll eventually be exploring in N4 and N3 lessons.

NOUN ＋ の ＋ ごとき + NOUN
NOUN ＋ の ＋ ような + NOUN

NOUN ＋ の ＋ ごとく + NOT-NOUN
NOUN ＋ の ＋ ように + NOT-NOUN

Also, remember that we can often translate all four of these (ごとき、ごとく、ような、ように) simply as "like" or "as" in English.

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生まれたばかりの子供は天使のごとく美しい。
うまれた　ばかり　の　こども　は　てんし　の　ごとく　うつくしい。
A newborn child is as beautiful as an angel.
Literally: "just born (=born + just) + の + child + は + angel + の + ごとく + beautiful."

Uh, I've seen some newborn babies, and most of them look like little monsters to me. But I try to avoid saying stuff like that in public, especially when people are showing me pictures of their newborn... uh, angels...

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Now, as often happens in lessons, we get to talk about something that confuses me:

彼女のごとき優秀な人は一刻も早く海外に出るべきだ。
かのじょ　の　ごとき　ゆうしゅうな　ひと　は　いっこく　も　はやく　かいがい　に　でる　べき　だ。
Someone as gifted as her should go abroad as quickly as possible.
Literally: "she + の + ごとき + gifted / excellent + person + は + as quickly as possible (=moment + も + quickly) + overseas + に + go out + should + だ."
Note: The nuance here is that there are more opportunities abroad for someone of her abilities.

I'm confused because I would have thought that we use ごとく since the word directly after it is a na-adjective, 優秀な (ゆうしゅうな // superior; excellent; capable; gifted).

So why did we use ごとき？

Well, I have two answers:

Answer #1: I don't know. In fact, I caught many Japanese people online writing "ごとく + na-adjective."

Answer #2: We can say that the ごとき, "like," is referring to the noun after 優秀な, which is 人 (ひと // person).

Anyways, this is the kind of stuff you don't need to be worrying about. If they actually try to test you on something as minute as that in JLPT N1, then the test-makers are evil human beings.

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Like we saw in the last example, here's another case of ごとき jumping over a na-adjective to describe a noun, もの (thing).

母の愛のごとき偉大なものはこの世に二つとない。
はは　の　あい　の　ごとき　いだいな　もの　は　このよ　に　ふたつ　と　ない。
There is nothing in this world that is as great as the love of a mother.
Literally: "mother + の + love + の + ごとき + great / grand + thing + は + this + the world + に + one and only (=two + と + there is not)."

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彼女は流れる水のごとくなめらかに踊る。
かのじょ　は　ながれる　みず　の　ごとく　なめらかに　おどる。
When she dances, she moves as smoothly as flowing water.
Literally: "she + は + flow + water + の + ごとく + smoothly + dances."

Man, I wish I could dance like water. I could make that my new career. Goodbye gym. Hello dance moves.

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Hey, you. Did you catch the two idiomatic phrases we had in the above sentences?

Here they are again. Learn them!

一刻も早く
いっこく　も　はやく
as quickly as possible
Literally: "moment + も + quickly."

二つとない
ふたつ　と　ない
one and only; unique; unrivaled; peerless
Literally: "two + と + there is not."

If you use phrases like this in your own speaking and writing, you'll sound pretty cool.

Well, if you're like me, you'll mess up the phrases somehow and almost sound cool. But hey, at least we tried...

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Time to end... with a quiz!

Do you think you can read all of the sentences we've seen so far without the translations?

What's more, can you read and understand them using not ごとき・ごとく but instead the more common ような・ように？

Let's find out...

地獄のような経験をした。

生まれたばかりの子供は天使のように美しい。

彼女のような優秀な人は一刻も早く海外に出るべきだ。

母の愛のような偉大なものはこの世に二つとない。

彼女は流れる水のようになめらかに踊る。

If you are really planning on tackling the N1, you should be able to handle sentences like these... even if you don't know a word or two that shows up in them.