Yup, you have it correct. Texas would maintain the same number in the House of Representatives, however Texas (once split into 5 states) would add 8 Senators (they already have 2, right?) and the USA would not be allowed to have a vote in the decision.
As a Texan, I can say with certainty that if Texas would split into 5 states, those states would be political lines only - at least for a few generations. Once a Texan, always a Texan. Oh, before I forget, if you accept Snopes as a source .... Source
see post 47