The consoles that give +5 to Astrophysicist, Anomaly and i think there are a few others are related to skills box under Starship Operations. In the 5th column (admiral) it gives the boxes with Astrometrics and Spatial anomaly. The description of these are a lot of what the +5 devices do, they boost stats of abilities related to Spatial Anomaly or Astrometrics.
For example Gravity Well is an ability the player can use, putting the device +5 Anomaly will boost ur Gravity Well ability in some way, Iím unsure in what way as I have not got that high in lvl yet. Itís not just limited to Gravity Well, its limited to abilities related to Anomalyís, which Gravity Well is.
At least this is how I currently understand how those consoles work. I could be wrong as this is just a guess based on what I have seen and heard others say about other ppls guessing.