We made an offer on a home that was about 5% below the asking price.  Our offer was rejected.  What can we do to make the owners more reasonable?

Who says the owners aren't reasonable? They have established a market price for their home.  If they can get that price within a reasonable time frame, then they have logically priced their home.  If the price cannot be obtained, they will lower either the price or the property will be withdrawn from the market.  Because your experience in a different market made selling at a loss acceptable, that does not mean the same logic applies in other markets, or that your choice should in any way impact the sellers.  Perhaps it would make sense to restructure your offer - maybe raise your price but seek better terms.

Thanks,

Aaron