What the difference?

[Pressman]

Hello! Can you tell me the difference between
to seek for sleep
and
to try to sleep
Many thanks

[Alan]

Try to sleep simply means make an effort to sleep but seek for sleep doesn't make sense I'm afraid. Seek as a verb means try very hard to get or find and is used in special cases in expressions like seek peace/help, which is a sort of formal or literary use.
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English as a Second Language
You can read my ESL story The Name of the Game