heh....this sounds all too farmiliar. When I bought my B16A2, the tranny had the same problem. But mine was from second to third instead of fourth to fifth. Since I am in Toronto, Canada, my pricing may seem a bit odd but here it goes....... Since the synchro's on B-series trannies come in packs of two (1+2, 3+4, 5), for me it was more expensive. Now I dont know for sure, but I think that 5th is a synchro on it's own (correct me if I'm wrong). It took my mechanic a total of 6 hours to do this job. 2H to pull the tranny, 2H to install the new synchro's, then 2H to put the tranny back on, top up fluids and everything else. The whole ordeal cost me $650CDN. inc. labour. I dont know if the 5th sync. is any cheaper than the rest, but it might be. Now I had the option of just replacing my tranny completely, and buying a used JDM B16 Tranny, which is probably what I would have done if I had more $. But everything works great now, and Im totally happy with the rebuild.
My advice: If you can afford a new tranny with a not broken synchro, then do it instead, but if you want this one, then that's fine too. It will most likely end up costing the same in the end.