Care to share your calculations?
First of all: I am not an expert.
10 bytes at SF8 take 114 ms air time to send. When repeating that every 5 minutes, you’d send (24 × 60) / 5 = 288 messages per day, totalling to 33 seconds. That’s just above the TTN Fair Access Policy, which is roughly based on 1,000 nodes per gateway (but also an average duty cycle of 5%, which may be high). Using that math, one gateway would suffice?
It might be stretching the limits though, if all nodes are using the maximum daily air time. On the other hand: on SF7 the air time would be about half of this.
When not taking the Fair Access Policy into account, but using a lower duty cycle of 1%, you could send 10 bytes at SF8 every 12 seconds (on the same channel). So, assuming it’s a good idea to keep the network’s duty cycle below 1% too, then when sending only once per 5 minutes while you could repeat that every 12 seconds, I guess you could support (5 × 60) / 12 = 25 nodes per channel, per gateway. With 8 channels, that’s 200 nodes per gateway, so would require 5 gateways for your 1,000 nodes?
It’s hard to come up with definitive numbers. As nodes just send when they feel like it, the duty cycle aims to lower the chances on collisions, also with non-LoRa signals. That’s also why, in the previous paragraph, I did not multiply the result by 100 to get to 100% air time usage. (For those 25 nodes above, the air time would only total to 25 × 114 ms = 2.9 seconds every 5 minutes, just below 1% of the available 300 seconds.) The overall duty cycle of the network could probably be higher without introducing too many collisions. But if all sensors would react to similar events, then they would transmit simultaneously despite the duty cycle. Also, adding more gateways assumes the network will tell nodes to lower their transmission power, to ensure only few gateways receive the transmissions of a given node.
Did I say I am not an expert?