I did a 2 month long course of Cerebrolysin where I would have to inject upwards of 10-20ml a day. Often times I had to buy large ampules and store the remaining liquid in syringes. I kept them in a ziploc bag in the fridge with the needles and caps on. I could make 3 needles and syringes last me a week (about 3 - 4 injections each). If you are gonna reuse a syringe (never tried needle) for more than a week, then rinse out periodically with alcohol and then distilled water twice. I personally got through my cerebrolysin course without any form of PIP or infection. As long as you avoid contact with everything, keep in the fridge sealed, clean your injection site, you should be g2g.
Obviously, no one can advocate this, because risk isn't worth reward (the price of needles and syringes nowadays), but after about 100 injections you kind of just get it done. I mean the amount of times I've eaten a girls ass or thrown pavement into my skin riding my BMX, or cut open my hand with scissors (and all the doc did was krazy glue it up, and sent me on my way), you can discern whether or not something will be dangerous to you and your body.
But to answer your question 3-5 days in the fridge in a ziploc with a cap on should be fine imo.