The Space Empires series has considerable nostalgic value for myself. I started out my "space management" games with Masters of Orion II (back in the day). Eventually I game across Stars!, a community, non-graphical space game. Home World, Pax Imperia, Gallactic Empires, Sins of a Solar (not quite the same, that one). Space Empires is the only series that holds to the classic MOO2 and Stars! style of TbT play, and it's one of the most easily modified games you're like to come across.
A lot of people prefer SE4 over SE5. I prefer SE5 myself, though realistically there's not a whole lot of difference to mechanics and style between the two. SE5 has a better graphics engine, but it's still not going to dazzle you. That's not what this series is about.
The game plays from the top-down or pseudo-3rd (my term for 3rd person bird's eye). Solar systems are set out on circular hex grids that delimit movement spaces, planet locations, etc. The objective is the usual: Take over the universe or (snicker) attempt to co-exist with the rest of the universe's aliens. But the primary design and intent is to conquer.
There's a ton of variety and ample room for customization (even without modding things). Smaller universes offer the quickest fix for action and conflict. But the universe can also be set up to be huge for those of us who like to play a more epic game session. Warning however! In this later case, expect your PC to start taking quite some time in between turns as it crunches out the numbers. Even my powerhouse PC was taking a minute or so after the turns started getting past triple digits.
The way you set up the game session will have a huge impact on play, so take the time to figure out the settings. One simple setting (and I forget what it's actually called) changes resources from percentiles to static, depletable values. This is a significant game-changer for longer games, as the asteroids & planets will eventually exhaust their resources, forcing you to expand in the incessant search for more. (Unless, of course, you some modding...there are some values on a few planetary improvements that regenerate resources...)
The A.I. can sometimes be downright stupid, and other times it can appear to be devious. I have trouble sometimes determining what is accidental and what isn't. However, there are a few quirks that make this A.I. predictable as well, especially concerning ship building and pathing through star systems. Ultimately, it makes the same mistake as so many other games in the "management" genre: the A.I. focuses on a war of quantity rather than quality or tactical/strategical considerations.
Amazing multi-player potential if you can set up a game. That's all I'll say about that.
So. Some discontent with the A.I., and a processor hog when things really get going in an epic session are the only cons in my opinion. But massive mod potential and out-of-the-box customization help create a different gaming experience every time. Multi-player is downright fun (but it's an older game, so you'll need to find some 'cultists' out there).