I have a total of 5 servers, so I'm thinking of maybe running an ES on each of them, forming a cluster. I would have more hard disk space then as well.
Yes, in theory you should see better performance the more servers you add. (You can in theory have multiple Elasticsearch instances on the same server, you'd just want to make sure that the disks aren't really shared, but if you have more disks in more servers, then in theory that would work as well).
One thing to note, you will want to adjust the index.number_of_shards on the index(es) you're using, by default, Elasticsearch sets this value to 1, which doesn't really "scale". You can generally set the value to the number of nodes you have in your cluster. (You can sometimes even increase this number more if you're not seeing resource utilization saturation to push things even further, though it generally has dimensioning returns).