Can I put a Nikon Ai or Ai-S lense with my D5300 ?

I know that it will not do any metering, auto focus anythign like that. But for pure manual use, Can I mount an Ai lense to my DX body?

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Yes, these are all F-mount lenses, and since all of Nikon's DX & FX DSLRs use the F mount, all of these lenses will all mount onto your D5xxx body.

Yes.