Does OnePlus 5 use the same screen as OnePlus 3/3T?
Sort of.

The OnePlus 3T and 5 share the same display model. Pocketnow even wrote an article about it.

However after further inspection, only some 3T phones have the display model of S6E3FA5 (This is the OnePlus 5's display.) Others are S6E3FA3.

Therefore, only some of OnePlus 3T's share the same display as the 5.

Can't tell for certain but from this forum post, the OnePlus 3 shares a similar story.