First, let me thank my colleague at Fordham University, Lance Strate, who recommended The Orville to me just last week. He has a pretty good track record, his best recommendation so far being the reboot of Battlestar Galactica, which was much better than the original and superb.
I'm tempted to say The Orville is to Star Trek: The Original Series as Battlestar Galactica 2004 was to Battlestar Galactica 1978, but that wouldn't be quite right, because: (1) The original Star Trek was one of the best series ever on television, and the first BSG was, if not one of the worst, certainly nothing special, and (2) Battlestar Galactica 2004 was so dark as to be apocalyptic whereas The Orville is laugh-out-loud funny.
That's not surprising, since Seth MacFarlane not only stars in this latter day Star Trek as Captain Ed Mercer but is the creator of the series. And the jokes are not only funny and continuous, with words like "dick" tossed around in just about every episode, but they don't interfere in the slightest with the outstanding science fiction in every episode, which was the strong suit of the original Star Trek.
In fact, I'd say The Orville is more like Star Trek the original series, truer to its pace and elan and sense of wonder, than any Star Trek since, with the exception of Star Trek: The Next Generation, which was in some ways better and some ways worse (and, come to think of it, The Orville is in some ways more reminiscent of the best parts of TNG and its interspecies-diverse crew than it is of TOS). But everything else that's come since, whether on TV or in the movies, is just not as good, whatever their redeeming qualities. (Ok, I only saw the first episode of Discovery, because I'm too cheap to pay for yet another streaming service, but that first episode was at best only all right in comparison to the first episode of The Orville.)
I won't summarize that for you - if you haven't seen it, do - but each of the five episodes I've seen so far packs a different kind of punch. To return to episode 5, it's not quite as good as "City on the Edge of Forever" from TOS or "Yesterday's Enterprise" from TNG -- which are about the two best hours of time travel ever on television -- but it's pretty close, has respect for all the paradoxes of time travel, and like almost all fine time travel, even a thread I don't quite get. When Kelly confronts Ed about telling the time traveler about Kelly and Ed's marital problems (they got divorced, because Ed found Kelly in bed with an alien who came in blue), Ed says of course the time traveler knew, she came from the future, and Kelly says no, our problem took place in the past, and Ed admits he told the traveler. But ... wait a minute, maybe that was a joke!
Kelly, by the way, is played by Adrianne Palicki of Friday Night Lights, and I'm always happy to see a star from that great series on TV again, just as I am about anyone from The Wire. The crew, by the way, consists of five humans (Ed and Kelly, a woman doctor, and two guys on the bridge or whatever that is), a younger officer who looks like a Bajoran (well played by Halston Sage), a Lt. Commander of some sort who looks like a Klingon (and lays an egg - not a bad joke, as Ed quips, but offspring), and some kind of highly intelligent android who sounds like Data but looks like the Tinman digital edition and maybe a little C3PO. There's also an intelligent kind of slime with Norm MacDonald's voice, but I'm not sure if he's part of the crew. These homages to Star Trek are of course deliberate and delightful, as is the music and the overall feel of the series.
Star Trek's back!
See also: The Orville 1.6-9: Masterful ... The Orville 1.10: Bring in the Clowns
1st starship to Alpha Centauri ... had only enough fuel to get there