The good advice in here is that you should always take a few days to consider an offer. I'd use that time to get into contact with some friends or favorable interviewers at the company and get some "off the record" time to get a sense of what kinds of projects you'll get. Project allocation is more important than a measly $5,000 in salary. If compensation is an issue, figure out if you're being paid fairly. Not, "What do you make?" but "What should I expect to make?" People will give you accurate numbers.

As for trying to claim another offer to get more pay... Bad idea! You're unlikely to have the offer retracted-- simply divulging that your offer was rescinded in the right corners of the internet will damage the firm's reputation in a way that is more costly than the cost of retaining you for a few months, but the "I have another offer" trick, if you use it to negotiate more compensation than you deserve, is going to damage your reputation among those who know you used the tactic. Yes, they'll hire you because rescinding an offer leads to negative press, but they won't like you much.

Also, firms that lowball are generally not places you want to work. It's a huge warning sign. I got an offer at a company that lowballed me, I negotiated a 25% increase, and went to work there, and it was still a mistake. My observation is that the initial offer gives you the best sense you'll ever get (better than performance reviews!) of what those in power at the company think of you. If you negotiate a higher offer, you'll get a little bit more cash, but won't improve their perceptions of you. So you'll get crap project allocation and a high salary. When layoff season comes around, guess who's at the top of the list?

A good company will pay you fairly regardless of your salary history and other alternatives, and likewise not be pushed around by high offers from, e.g., Wall Street, an industry that throws money at people so they ignore its deep cultural problems and generally low quality of work.

If you want to negotiate a higher salary, there's a right way to do it and a wrong way to do it. The wrong way is to say, "I have an offer at Goldman Sachs for 50% more", to which most self-respecting recruiters will say, "Then go work at Goldman." The right way is to say, "according to my research <don't disclose what your research is, especially if it involves people at the firm> the proper salary for a person of my position is $<X>. I also believe that I have considerable long-term potential both on the technical and executive ladders, so add 10%. Also, I don't need the 10% hiring bonus upfront so why don't we just include that in my salary, which allows you to pay it on a later schedule. So $<1.2X> is what I consider a fair number." The negotiation needs to be about what you can do for them, not what you can get from a competitor.

You claim another offer to expedite hiring processes and to have leverage to ask for more insight into the work you'll be doing (and for more interesting work, to the extent that such things can be bargained). What you want to show is that you respect yourself and are looking for the best fit for you and your career, not that you're a mercenary who is only going to be there because of $5-10k in marginal compensation. People talk more than they should and you can get a negative reputation before you start if you do this.