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Can you get UK citizenship after 5 years of non-domiciled residence?

Citizenship - no.
But if you only need a tax residence - you can be a dependant on someone else's visa (wife/husband/partner) and spend as many days as you want in the UK as long as main applicant maintain the visa requirement (usually half a year+ for ILR and 276 days on average for the citizenship in the last 5 years).
There will be different requirements for
1) tax residence (that you need to move your tax affairs to the UK and utilise a remittance basis)
2) ILR
3) Residence

But if you only need a tax residence - it can be done with less than 183 days of presence in the UK.