this the plea agreement I made with the District attorney = the People
have made you the following offer, five years formal probation, three
years prison suspended and time served at time of probation and
sentencing

In UK law I would take this to mean:

five years formal probation = said person is on probation for five years

three years prison suspended = said person is sentenced to three years
imprisonment if said person breaks any (non misdemener) law during the
probation period

Basically, if said persion is well behaved for a while there's no prison stay.

The statement means.

The person will be on probation for 5 years.

If the person breaks there probation within the 5 years then they will
be sent to jail for 3 years.

If the person has already spent time in prison then this will be
deducted from the 3 year prison sentance.

or

If the person breaks probation then any time they spend in prison
prior to a court hearing and being sent to prison will also be
deducted from the 3 year sentance.