Hi @obvdan ,
According to the User manual for a Blu Studio Selfie it can take videos using the phone's camera app.
Scroll down to the Camera section in the manual for details.
You may need to insert a SD Card (64GB Max.) because of the storage requirements of large capacity pictures and videos.
Apologies. Initially, just read your question title and overlooked that it changed in the body of the question from video to screen.
You may have to root the phone as Android 5.0 (yours is 5.1) has a native API which allows screen recording, (or mirroring) when coupled with an appropriate app. This may have been removed by Blu.