It is important to remember that the reason you study chord patterns like 2 5 1’s is so you will be able to play freely over the changes to real songs. To learn to play Jazz well, you will need to know lots of popular songs which have become standards.
There are many books available which are compilations of standards, often combined with more contemporary tunes. Probably the most famous of these is "The Real Book". Staff in most music stores will know about this book and it is recommended that you purchase a copy, or a similar book and learn the melodies and chord changes to as many standards as possible.
It is also essential to practice improvising over the chord changes to standard songs as often as you can, so that when you get together with other musicians, you have something in common to play. It is important to practice jamming with other musicians regularly, particularly a keyboard player or guitarist who can play the chords while you play the song’s melody and then improvise over the changes.
In the Bebop era, musicians began to write their own melodies over the chord changes of popular songs. The chord changes became the standard thing, with melodies being interchangeable. Try learning the chord changes to a song and then writing down your own melody to play over them. The following solo is based on the chord changes to Jerome Kern’s "All the Things You Are", which is a popular Jazz standard. This solo makes use of both modes and arpeggios. Analyze the notes against the chord changes and then make up your own phrases based on the ideas presented here. Memorize any phrases you particularly like, and then play them in all keys.