I'm using a p-channel mosfet to switch a 3.5V load, using a gate voltage that's ~5V. The gate goes from 5V to 0V, but the mosfet doesn't start conducting. Did I just fry the mosfet by having the gate be above the source, or is something else happening?
It is OK for this MOSFET to have the gate higher voltage than the source. The data sheet says that the part can handle +/- 25V on the gate.
Note that the 2->4V spec is the range of gate->source threshold voltage for just barely turning on part to 250uA of drain current.
The gate voltage is referenced with respect to the SOURCE terminal of the part. If you are attaching the source to a 3.5V supply and with the load then connected from the DRAIN to ground then you are going to need to have a gate drive that is at least 4V below the 3.5V level to get the FET to barely turn on. If you want to achieve the data sheet specified low RDSon of 0.055 ohms the gate will need to be -10V with respect to the source or a whopping 6.5V below the ground level.
Like somebody said in the comments. This FET and your driving configuration are not suitable for switching a load on and off from a 3.5V supply. Come up with a negative rail to swing the gate to and then it might work.