Do you know if there is any way to upgrade my current Lightroom 3.5 to newest Lightroom 5?
Yes you can. I just asked Adobe and was told that it is possible, at a cost of approximately $75.00
Edited: It seems that you can upgrade from Lightroom v1.x, v2.x, v3.x and v4.x to v5 for the same price (upgrade and not full software). Last time I checked I haven't found this possibility. Good news for everyone :)
Regarding your Lightroom software v3.5, installing Lightroom 5 will not modify your 3.5 installation (you will still be able to launch Lightroom v3.5).
Regarding your Lightroom catalog v3.5, Lightroom 5 will create on installation a copy of your catalog v3.5 and "upgrade" it to v5. Look here for more detail.
If you have any doubt, copy your catalog v3.5 somewhere else before installation.
More detail on updating Lightroom from vxxx to v5 here.
For information, Lightroom 3 and Lightroom 5 aren't using the same Process Version. You should probably read about it so you won't be surprised.