Looking for 5-port "switch-like" gigabit router with vlan support

Why not go for a small managed switch which would solve your VLAN requirement while still falling inside your cost envelope.
You might also want to read:

as there might be a suitable switch that can be flashed to run OpenWrt, however I am not sure whether these fall within your size requirements.
(When I had to get a switch I went for a model I could install OpenWrt on (Zyxel 8 port managed POE switch), but so far just operate it under Zyxel's OS as it is just a switch)