After remaining in China for more than 5 years you are no longer a foreign expert, but a Chinese one.
You can however apply for a Foreign Obsolete Certificate.

Ignore visa touts like tiffany above, they don't understand the underlying issue.

But I do--it has to do with foreigner taxation (IIT-individual income tax), and I'll oversimplify a bit. Basically, when you are a resident foreigner working legitimately (work permit or FEC), you are subject to taxation on all your China-sourced income (China job, income from renting a China property, etc.). After 5 years, Chinese law makes a resident foreigner subject to Chinese IIT taxation on their worldwide income, which gets into another level of complexity. That you and your employer won't want to get into. This is why your employer is only willing to get/keep you legal up to the 5 year time limit, which is this coming summer. (2006-2011)

Most expats--especially corporate people on larger salaries and with income from other sources outside China--know about this and avoid being here more than 5 years continuously. How do you do this? Well, Chinese law on this actually makes it easy to do--what you need to do is either:
(a) Leave the PRC for 30+ full days continuously in any calendar year...excluding the travel days in/out of the country. Continuous means just that--leave for a month plus and don't come back til after that; or
(b) Be out of the PRC for 90+ days cumulatively in any calendar year...also excluding travel days. The 90+ days can be done in pieces.

Either of these maneuvers in effect, breaks the Chinese legal definition of "continuous residence" and resets your taxation clock basis back to Year 1. Quirky, but I've done it a couple of times with my last "reset" in 2008. You can go anywhere you wish for your temporary exile, as long as it is outside the PRC.

It's actually best to do this reset before getting to the very end of the 5 year period, as you are about to find out. This is so that you can get a renewed work permit/FEC/residence permit without having a complete break in your paperwork. If you get to the end of your current visa/permits and then leave the country for your exile, you may have to jump through all the employment hoops again (medical, etc), just as if you were a new expat arriving for the first time. Unless your school/organization has some kick-ass guanxi and can shortcut some of the usual process. My practical suggestion is to work with your school to see if you can take an extended Chinese New Year holiday--maybe find a substitute short-termer to take your place for days you'll miss. They might be willing to do this, especially if you and your school hit it off well, they want to keep you, and you want to continue on with them beyond the summer.

If you can manage to do that 30+ day exile, then come back and they should be able to do a normal 12 month renewal of all permits and FEC at any time after your return. If your intention is NOT to continue on with them but come back to China, then you might wish to just leave things alone, leave when your contract/paperwork expires, stay out 30+ days on a natural holiday, then return and jump through the usual hoops with a new employer. In this case, you might want to get a new position under contract before you leave your current one, and from the new employer, get the paperwork needed to get a Z visa in HK (or elsewhere), which you'll use on your return to China at end of summer. Don't forget that release letter from your current employer, get it before you leave.

This issue isn't a PSB Entry & Exit Administration issue, but something your school is imposing on you. The PSB doesn't care about your tax issues and if you are willing to subject yourself to total Chinese taxation on your worldwide income, then so be it.

First of all, the only thing you'd have to worry about is if you have income abroad subject to Chinese taxation. If you do, then you have to consider how the heck the Chinese tax authorities would even know. If you are, for example, a US citizen, it is virtually impossible the IRS would share any tax data with Chinese authorities. Of course, you can declare the income if you want, but if you do not the risk is virtually nonexistent.

If your school is willing to give you 30 days off and you can find somehwere outside of China to spend them, maybe it saves you a little hassle. But if your school is willing to process your visa in spite of not leaving for 30 days, you have very, very little to worry about.

I find it amusing, but not surprising, that Dezan Shira would state:

That statement is false, as is much of what comes from those morons. They make it sound like when you leave China you will be given the third degree over tax issues and it simply will virtually never happen -- especially in your situation.