Keep in mind I'm a mass shipper, so even if I don't mention a ship, there's a high chance I ship it or at least enjoy seeing it once in a while...and with that said : here are my #Top5Ships in chronological order :

#Solkat (Homestuck)
#DirkJake (...also Homestuck, to be fair there are a shit ton of characters and thus shipping possibilities)
#TanuNatsu (Natsume Yuujinchou)
#sormik (Tales of Zesitiria)
#shizaya (Durarara!!)