Can I run TinyLlama-1.1B-Chat-v1.0 on an RTX 5090?

Yes

Its published weights (2.20 GB) fit in the 28.8 GB an RTX 5090 can use, with room for ≈ 2K tokens of context.

hf download TinyLlama/TinyLlama-1.1B-Chat-v1.0

Files and context on RTX 5090

Each file of TinyLlama-1.1B-Chat-v1.0 (and of GGUF versions the site has analyzed), and how much context fits next to it, with the context cache in 16-bit or 8-bit.

TinyLlama-1.1B-Chat-v1.0 on other hardware

Popular models that run on RTX 5090

Assumes 90% of the card's memory is usable and at least 4K tokens of context for one conversation, with the context cache in 16-bit unless noted. Fits leaves at least 20% of that memory for context; Tight leaves less.