Hi and yes.
You do this:
1) Download ios 5.0.1 ipsw (you can check the forum for a pinned post with all ipsw files, you choose the right one for iphone 4)
2) download redsn0w 0.9.10b4 (you can find on google)
3) You run redsn0w - EXTRAS - CREATE CUSTOM IPSW and it will ask you to select a file, you select the 5.0.1 ipsw that you have downloaded
Then it will create a custom for you (the custom ipsw file name will start with NO_BB)
4) Then you go to itunes, hook up your phone and holding down SHIFT button on your keyboard, click on RESTORE.
A window will open up, and you will select the NO_BB ipsw that you created and you click OPEN.
The restoring process will start. Once it is done, your phone will be on ios 5.0.1 and with a preserved baseband.
Now if you want to jailbreak as well, you can use redsn0w (the same one), go to "Jailbreak and Install Cydia", and turn off your phone and follow the instructions, and tick "install cydia" (and nothing else) when asked.
If you need any help or have any questions please let me know.
Are you using a Gevey sim?