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I have been living in the UK for a about 5 years without any break under Tier 4 dependent. I have been working full-time and paid tax all these years. I was wondering whether I am eligible to apply for ILR or not.

Thanks for your help.

No you are not. Tier 4 or dependent does not lead to ILR based on 5 years residence. You also don't qualify for ILR without your partner applying if on a PBS route (tier 2 or tier 1).