I checked every flight yesterday on United from Heathrow, and all of them landed in Terminal 5. You have to clear immigration and customs in Terminal 5, recheck your bags before leaving the customs area, and then get to Terminal 1. If everything goes well, assuming you are a US citizen (Houston on profile) you will "probably" be ok. It can take a long time to get through immigration/passport control, so much depends on how many other flights land at the same time as yours. You cannot stay behind security to get to Terminal 1. You must take the tram to Terminal 1 for your next flight, which will be three stops from 5 (there is no 4) and go through TSA there. Again, much will depend on whether there are lines at that point as well.
This also presumes that you are flying on one ticket and aren't booked separately. If that is the case and you do miss the connection, then United will get you on the next available flight (note this may not be the next actual flight - they will not bump someone off the next flight for you).