Should I Accept an Offer with Contingency?

[Tony Castronovo]

I have had a property I am flipping on the market for about 110 days.  Originally priced it too high and it bit me in the butt.  Have since dropped the price to align with the market and have had two contracts, each falling apart for different reasons.  Just received an offer last night, but has a contingency tied to the sale of their existing home.  The buyer just put their home on the market 8 days ago.  It looks "ok" but not a home you would think would sell immediately (priced reasonably).  If I can't close by July 31st I will need to refi the home from my hard money loan.  And I would need time to pull the loan together.  My buyer is suggesting they can close by July 5th.  But they don't even have a contract.  Should I try to work with them (e.g. add a bump clause) or decline the offer?