I've LR 4 on a windows PC running. Now I bought a MAC and I'll buy a LR 5 upgrade. Can I install the upgrade LR5 without installing the v4 first?
Yes, you can.
You'll need your old Lr 4 serial number as well as the Lr 5 serial (both are asked for in an upgrade), but aside from that you should have no problems - Lr licensing isn't platform-specific.