f/5.6 will cost you. Relatively inexpensive and easily found ~90 mm lenses that barely cover 4x5 include 88/6.8 B&L, 90/6.8 Raptar and Optar (same lens, different engraving on the trim rings) and 90/6.8 Angulon. The first two are four elements in four groups double Gauss types, the Angulon is, well, an Angulon (6/2). All have much the same performance.
If you want movements too, look for a 90/14 Berthiot Perigraphe Ser. VIa. These lenses are all in barrel, if you need a shutter find a cheap Alphax #3 or Ilex #3 that works. Cheap is easy, that works isn't. These lenses can be stuffed into the fronts of these shutters. The Ilex is a better fit, the Alphax will need to have a little tape on the threads.