i have some lb broth for about 4 to 5 days old in fridge 4 c.

can i make there glycerol stock and also can i use them for growing new cultures.

confusion. how long a cultre can be placed in fridge 4c without glycerol.

I've kept cells for a month without glycerol, but obviously not advisable as most cells die once it runs out of nutrients.

You can use your glycerol stock to make a new stock. All you really need is to scrape some off your glycerol cell stock with a heated loop or pipette tip and put into LB media.

Take some of your refrigerated culture and culture for several hours, then make your glycerol stock from that.
It was my understanding that glycerol is added to a culture prior to freezing to help prevent ice crystal formation, therefore there is no need to have glycerol added to refrigerated stocks, however I do agree with tsng that long term storage of bacteria at 4C is unadvisable.

I agree with the others. There is no need for glycerol when storing at 4C -- glycerol is a cryoprotectant, and therefore is useful when freezing cultures, not when refrigerating them.

A good number of your cells at 4C will likely still be alive. Just swap the order of your intentions -- use the 4C cultures to start new ones, and make glycerol stocks from these new cultures.

As for how long a culture can retain viable cells at 4C, it depends greatly on the strain of bacteria, the media they're in, the density of the culture when stored, etc. But such a culture should retain some viability for a few days at least, several weeks at best.