I was wondering if there is a way that I can connect my laptop to the Internet using dial-up, and then connect my cell to laptop via infrared to let my cell phone (Nokia 5100 GSM) use the dial-up connection to browse the internet.
I do not think you can do what you are asking: Use your laptop to provide Internet access to your Nokia 5100 phone. Your phone is, after all, a network access device. But you can do the inverse: Use your Nokia 5100 phone to provide Internet access to your laptop. That configuration is supported by Nokia's PC Suite software, which lets your laptop use your Nokia phone as a modem when the phone is connected to the laptop by either USB cable or infrared wireless. To learn more, check
Nokia's Web site
5100 modem guide
You can also PC Suite to synchronize certain files from your laptop onto your phone. You could use synchronization to download files (e.g., ring tones, audio files, images) from the Internet to your laptop over dial-up, and then copy those files from your laptop to your phone over USB or infrared.