Of the 95 members of the 1st US Congress, 21 (~22%) of them were members of the 5th US Congress, with the following breakdown:
* 5 senators (~17%) remained senators;
* 9 representatives (~14%) remained representatives; and
* 7 representatives (~11%) became senators.
Notes: John Brown was initially a representative of Virginia, then later became a senator of Kentucky (which was part of Virginia at the time of the 1st US Congress). William Smith (MD; 1st US House), William L. Smith (SC; 1st US House), and William Smith (SC; 5th US House) were all different people.
Method: moderately careful transcription plus grep, perl, sort, uniq, and comm.
EDIT: Thanks for adventured for the correction. I mistranscribed Philip Schuyler's name when copying down the members of the 5th US Congress.
[0] I didn't independently check the lists on Wikipedia[1][2].
[1] https://en.wikipedia.org/wiki/1st_United_States_Congress
[2] https://en.wikipedia.org/wiki/5th_United_States_Congress
James Gunn (GA), John Henry (MD), John Langdon (NH), Philip Schuyler (NY), Theodore Foster (RI)
The short answer is: Federalists voted for it, and Democratic-Republicans voted against it.
If I'm reading the House and Senate Journals correctly, the relevant legislative history is as follows:
1. 1798-06-08: The Senate approves the bill. https://memory.loc.gov/cgi-bin/ampage?collId=llsj&fileName=0... https://www.govtrack.us/congress/votes/5-2/s99
The bill passed by a vote of 17-6 (GovTrack reports this as 16-7 for some reason). Of the 12 members of the 1st US Congress who were senators in the 5th US Congress, two (John Henry and John Vining) had resigned well before the summer of 1798, and four (James Gunn, John Langdon, Philip Schuyler, and Theodore Sedgwick) did not vote on the bill. The remainder voted on straight party lines:
* Affirmative: Theodore Foster, Benjamin Goodhue, John Laurance, Samuel Livermore. (Federalists)
* Negative: Timothy Bloodworth, John Brown. (Democratic-Republicans)
2. 1798-06-21: The House approves the bill, with amendments. https://memory.loc.gov/cgi-bin/ampage?collId=llhj&fileName=0... https://www.govtrack.us/congress/votes/5-2/h90
The bill passed by a vote of 46-40. Of the 9 members of the 1st US Congress who were representatives in the 5th US Congress, one (William L. Smith) had already resigned at the time the bill was considered, and two others (Thomas Hartley and Josiah Parker) did not vote. The remainder voted as follows:
* Affirmative: Abiel Foster, James Schureman, Thomas Sinnickson, George Thatcher. (Federalists)
* Negative: Abraham Baldwin, Thomas Sumter. (Democratic-Republicans)
3. 1798-06-22: The Senate concurs in the amendments. https://memory.loc.gov/cgi-bin/ampage?collId=llsj&fileName=0...):%230020505&linkText=1
Either there was no vote here, or the yays and nays were not requested. The Senate Journal just says that they took into consideration the amendments and resolved that they concur in the amendments.