I have not tested the software at the sourced link (I do not own a Nokia 5310), so I encourage you to be cautious. It's Free, though!
Source(s):
http://www.topshareware.com/Nokia-Free-Unlock-Codes-Calculator-transfer-420...

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try it this tell me whether it helps you

http://www.metacafe.com/watch/331048/hack_nokia_password_security_code/
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I know that you are looking for a free solution, but in case you don't find what you were looking for or if using some free software or tricks has left you with an unusable or bricked phone, I would recommend the services offered by the DA VINCI TEAM. They're great. Unlocking, de-branding, re-branding, re-flashing, updating or installing firmware of a different region (e.g. if you want Russian or Thai menus and dictionary)... I have tried various services and whenever I used Da Vinci Team, it always worked perfectly. As a European company based in the Netherlands, they are confronted with hundreds of network providers and thousands of phone models for many years. Therefore, they are much more experienced than services in the US where GSM phones are relatively new and there are just a small number of networks. Just have a look at the vast list of available firmware versions they offer. I'm pretty sure that many of the competing unlocking and de-branding services are just re-selling DaVinciTeam's services. In most of the cases, you need just the USB cable that you got with your phone and a PC running Windows. Unlocking/De-Branding your 5310 will cost Euro € 10.- or about USD $ 14.- I have used it mainly for SonyEricsson phones. But your Nokia 5310 is in the list, too. This is how flashing a Nokia looks like with their software:
Source(s):
http://www.davinciteam.com
https://davinciteam.com/1/faq_73.html

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Looks like Davinciteam haven't broken the BB5 on Nokia handsets yet, so their software can flash software and de-brand handsets, but cannot unlock SIM lock.

The BB5 baseband that newer Nokia models use is still pretty much unlockable. You might find it easier to contact your network provider (who the phone is locked to) and obtain the unlock code from them.
Another solution is to use one of the piggyback type SIM wafers, however these alter the information the handset provides to the network and therefore may not be legal to use.
I have one of these http://www.dealextreme.com/details.dx/sku.13480 and it works OK. Again, very questionable legally.
Source(s):
http://www.dealextreme.com/details.dx/sku.13480

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I hope this article would help you:
http://www.wikihow.com/Unlock-Your-Nokia-Cell-Phone
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