Since I'm also currently planning some Russian flights for myself, I will try to provide a summary here:
on Saravia, a safe bet, as already mentioned by airevents.
on Saravia, a safe bet, but daytrip only possible in combination with Rusline CRJ on certain days
on Izhavia, also a safe bet, worst could be a change to Tu-134, but impossible to book from outside Russia, also combinable LED
on UTAir (possibly operated by Gazpromavia) until 31Dec (showing as Tu-134 from 01Jan)
on Gazpromavia, probably a safe bet, but Gazpromavia also has 73G in the fleet, also possible in combination with Polet SF3/S20 (airport change required from ULY
to ULV) and/or UTAir AT7
on Grozny Avia, a safe bet equipment-wise, but nightstop required, GRV is not the place to spend a night
VKO-LED-VKO on Gazpromavia, every Fri/Sun evening, turnaround not possible due to short ground time, but easily combinable with any other MOW-LED-MOW flight
VKO-OVS-VKO on Gazpromavia three times weekly, but only 1:10 turnaround in OVS, no other flights to combine with
on AkBars Aero, probably safe, but AkBars also has CRJ's in the fleet
on AkBars Aero, but only with nightstop in JOK or TBW
on Severstal - too late! - schedules already showing CRJ from 20Dec! Before that daytrip possible Tue/Thu on the Yak-40, but CRJ may be phased in earlier?
on UTAir from 01Jan
on UTair only as a nightstop in SCW, other frequencies on 737 (as mentioned)
on UTAir, only 1 hour turnaround, no other flights (IGT = Magas, Ingushetia = a new IATA code)
on UTAir until 24Dec (after that CRJ), nightstop required
on Dagestan/South East, but turnaround in MCX only 2 hrs, probably same a/c but check-in maybe
closed already in case of delay
on Alrosa on Wed until end of March, but on a couple of dates it won't operate
on Gazpromavia, not daily, early dep from VKO
(around 0300lt), route operated with mix of TU5/73G
on Avialinii Mordowii, nightstop in SKX required
This is by no means a complete list. I'll add to it when I find more. There are probably also some more flight to destnations farther away, such as Siberia (Alrosa Tu-154, for example). But those are quite expensive.
Edit: two more Yak-42 options added.
@Birdwatching: I realize you asked for May specifically, but maybe the information is also of use for others, planning a similar trip early. May may just be too late.
[Edited 2011-12-02 09:27:22]
[Edited 2011-12-02 09:30:10]