Rode NTG2, AT897, or Sennheiser MKE600 are decent interference tube mics considering their low price. But they will have some self noise.
Depends on "affordable". I'd go with a used Sound Devices MixPre (first version seems to go around 500USD). There might be some less-expensive boutique equivalents out there, but i don't have any specific reference in mind right now.
Is the preamp noise on the H5 so bad (send us examples)? What mic is used with it ?