How how can I convert UK used iPhone 5s to work with Nigerian sim?

iCloud username and password has nothing whatsoever to do with this.

If you want to use the phone in Nigeria and it is locked to a network in the UK, then you need to approach the carrier in the UK that the phone is locked to and request that they unlock the phone for you.

Nothing more to do than that - contact the carrier and put in an unlock request - the carrier and only the carrier can unlock the phone for you.

please am in Nigeria and i have an iphone 4 which does not have nigeria network becuase it was sent from UK i reseted it and am stocked to the activation menu it's asking for a supported sim i have nearly tried all nigerian sim but not working please help me

As indicated in the earlier posts, the device is locked to the UK network it was used on. You will need to contact that carrier, see if they provide unlocking services and if you qualify. Then follow the instructions they provide. Once the device is unlocked, you will be able to use it with your SIM.

Was it unlocked from the UK carrier? What error message do you see when you put your sim in it?