The IPS1031 will work at lower values of Vin. Look at fig 5 on the datasheet. The Rds at 3.8V would be about 125% of the 5V Rds but still quite usable. Note: I find this to be an odd part as it doesn't use standard MOSFET terminology - Vin appears to be Vgs. Few disti's carry it (not mouser or digi). One word of warning - the diode drops may push Vin too low.
However, the IPS1031 seems like massive overkill to me. a simple logic level MOSFET like the IRL510A ($.80 or so) would work ok and be cheaper. I try to pick devices that are readily/widely available.
But even cheaper would be a small signal NPN like the 2N3904 (< $.10). If your load really is 5K (which I kind of doubt - that's only 2.4mA), then the NPN would be fine unless it needs exactly 5V. Heck, the PIC could source that current no problem.
why use a IPS1031/MOSFET/NPN to drive LED D2? the PIC can source/sink all the current you need.
R7 and R8 are too small. You will get something like 66 mA when you want more lik 20 mA. try 470 or 510 (standard values).
I'm not a fan of the LED across the relay coil (D1). It increases the work that the switch has to do. I'd use a seperate NPN to drive it but it's not necessary.
Finally, I'm not sure why you are using the structure you are. why not simply have one PIC pin enable the relay and one control the load. Your logic will be slightly different but you get rid of D3, D4 and R2 and simplify the circuit.