Maybe this isn't intercity enough, certainly not long distance but the five in no particular order would be
1. SF - Sacramento. Not the capitol corridor, which leaves every hour and goes south to san jose before going to SF. Rather, transbay terminal, a bridge to oakland, then north, with IC style commuter service.
2. NJ Central--restore some of the cross state lines that went through elizabeth and newark to Communipaw Terminal, with ferries to BKLN and staten island, and a tunnel to world trade center. Now you have multiple direct trips from Morristown and northwards direct to downtown, and a 15 minute direct connection to newark liberty airport. plus, the NEC could now have some trains go downtown instead of NY Penn, which would help commutes into BLKN and make Penn less of a shitfest.
3. New HSR alignment between Boston and NYC. Fuck Connecticut NIMBYS who fought electrification and are now fighting a removal of the line from the coast inland. Also fuck Metro North for capping speeds at 50 MPH. Boston to NYC should take 1.5 hours direct on a dedicated HSR line, which Amtrak would be building right now if not for NIMBYS.
4. Make the Merrimack Valley line great again. Seriously, there are some great towns (Haverhill, Nashua, Lowell) which should be a fast, regular trainride to Boston, instead of the shitfest we get with Keolis/MBTA. While we're at it, electrify ALL the MBTA commuter rail lines. Massachusetts should return to being a bunch of cute rural towns connected to the city by regular rail service.
5. Willamette Valley to Seattle. Same theme here--not occasional Amtrak service, but real InterCity service on electrified lines.