I would like to practice with the actual orchestra (or even something synthetic) in the background to see if I can actually play at tempo. I'll never be in a position where I would be able to play it to an audience but would be awesome to see if I can do it...and maybe someday record it for the grandkids...
The Music Minus One publishing company and record label has been making recordings like this available since 1950.
They have exactly what you want, here.
Music Minus One Piano: Beethoven Concerto No.5 in E-flat, op. 73 (2 CD set)
Includes a high-quality printed music score with informative liner notes; and a digital stereo compact disc, voluminously indexed for your convenience, containing a complete version with soloist, then a second performance of the orchestral accompaniment, minus you, the soloist; and a second compact disc containing a -25% reduced-tempo version of the accompaniment for practice purposes. Musicians:Performed by Milena Mollova, piano Accompaniment: Plovdiv Philharmonic Orchestra Conductor: Nayden Todorov
You can find more products like this, including Mozart and Rachmaninov piano concertos, at musicminusone.com.
The entire concerto is available as a Standard MIDI file (SMF) for free.
If you are adept at working with Standard MIDI Files and have a DAW (digital audio workstation) or orchestration software package for your computer, such as Apple Garage Band or Cubase, Finale or Sibelius, etc., you can download free standard MIDI files of the orchestral and piano parts of this Beethoven concerto and make your own "virtual instrument" accompaniment tracks to rehearse and record to.
The ClassicalArchives.com website makes these free to download if you sign up for a free membership. Look here and scroll down to "Piano Concertos" and you will see the files available for your concerto.
The results you would get from this method wouldn't sound very realistic compared to the Music Minus One recordings, but you might enjoy the process of creating your own accompaniment. Furthermore, regardless of how good it sounded, with any suitable DAW you could manipulate the tempo to be as slow or fast as you want, and easily loop certain sections you need to practice on, for rehearsal purposes.