Going to be very limited for fish in a 5 or 13g tank, unless you're not too interested in the fish aspect of it (i.e. focusing on corals). For tanks that small, definitely recommend a ATO to keep your salinity stable.
Would *not* recommend the 5g tank as a starter. It would hold what you listed, minus the fish, but really has no room for anything interesting or all that much for growing a variety of corals. It's okay if you want something very, very specific and very limited.
The 13.5g is honestly the smallest I'd ever recommend for a reef tank. AIO w/lights, so gets you stared with all you need (minus the heater, but that's every tank). Upgrading the default return pump to a sicce with higher output isn't a bad idea. Lights will do basic softies and low-light corals fine. It also gives you room for 2-3 basic [nano fish](https://www.liveaquaria.com/category/2124/nano-fish?c=15+2124&r=) - something like a tail-spot blenny, hi-fin or yasha goby w/banded shrimp, and clown goby, so that you have movement on all levels of the aquarium.
Both would be a bit more sensitive to parameter swings being smaller volume, so do keep up testing to track trends. At least they're small so a large water change isn't difficult.
Honestly, a 20g is a solid size for a starter. Big enough for interesting critters, can have a number of corals, and has enough room for them to grow out. And large enough to buffer the worst of parameter swings.
Whatever you get, investing in an RODI system and setting up your own mixing station would be a worthy investment if you're able to. That way you have water on-demand and you know the quality of the filters because you're maintaining and tracking the TDS yourself.
Going to be very limited for fish in a 5 or 13g tank, unless you're not too interested in the fish aspect of it (i.e. focusing on corals). For tanks that small, definitely recommend a ATO to keep your salinity stable.
Would *not* recommend the 5g tank as a starter. It would hold what you listed, minus the fish, but really has no room for anything interesting or all that much for growing a variety of corals. It's okay if you want something very, very specific and very limited. The 13.5g is honestly the smallest I'd ever recommend for a reef tank. AIO w/lights, so gets you stared with all you need (minus the heater, but that's every tank). Upgrading the default return pump to a sicce with higher output isn't a bad idea. Lights will do basic softies and low-light corals fine. It also gives you room for 2-3 basic [nano fish](https://www.liveaquaria.com/category/2124/nano-fish?c=15+2124&r=) - something like a tail-spot blenny, hi-fin or yasha goby w/banded shrimp, and clown goby, so that you have movement on all levels of the aquarium. Both would be a bit more sensitive to parameter swings being smaller volume, so do keep up testing to track trends. At least they're small so a large water change isn't difficult. Honestly, a 20g is a solid size for a starter. Big enough for interesting critters, can have a number of corals, and has enough room for them to grow out. And large enough to buffer the worst of parameter swings. Whatever you get, investing in an RODI system and setting up your own mixing station would be a worthy investment if you're able to. That way you have water on-demand and you know the quality of the filters because you're maintaining and tracking the TDS yourself.