Tsavo East is the largest national park in Kenya and together with Tsavo West the closest park to the coast. Therefore, these parks are also possible as a short-term safari from the beach hotel.
Are there red elephants? Yes, you can find them in Tsavo East. They powder themself in red soil which will give them that great color. The elephant density in the park is quite high and giving you a good chance to see the red elephants.
All Big 5 should be present in the park, but the total animal density is not so high, so the chance of seeing them all is not the best.
Available animals: https://www.safaribookings.com/tsavo-east/wildlife