I've got a similar pair of Epicure Model 4. The difference is bigger cabinet and woofer in the 4 vs. the 5. Nice speakers, nice sounding. Make sure you check the foam surrounds. Yours look good, and maybe they've been recently redone, I can't tell from the pic.
kfa888, yes, they do look similar to the woven material in your Altecs, but the Epicure woofer is actually molded out of VERY thin styrene, and that "waffle" pattern helps give them stiffness.
Incidentally, I recapped my Model 4 crossovers with Dayton polypropylene caps, and since I had a few of that value lying around, I matched them EXACTLY with my DMM (yes, mine can measure capacitance), and the way they imaged after was REALLY nice!
Recapping the crossover isn't expensive, there's only one in each speaker!

Mr. Burhoe was a genius when it came to building drivers and cabinets that worked well together, and required a minimum of crossover components. And often, the resulting sound was spectacular, especially given the era most of them were built.