In MySQL, the easiest way is to use variables. The following gets all sequences of days with 100 or more pushups:
select grp, count(*) as numdaysinarow
from (select (date - interval rn day) as grp, td.*
from (select td.*,
(@rn := if(@i = id_user, @rn + 1
if(@i := id_user, 1, 1)
) as rn
from trainingdays td cross join
(select @rn := 0, @i := NULL) vars
where number_of_pushups >= 100
order by id_user, date
) td
) td
group by grp;
This uses the observation that when you subtract a sequence of numbers from a series of dates that increment, then the resulting value is constant.
To determine if there are 5 or more days in a row, use max()
:
select max(numdaysinarow)
from (select grp, count(*) as numdaysinarow
from (select (date - interval rn day) as grp, td.*
from (select td.*,
(@rn := if(@i = id_user, @rn + 1
if(@i := id_user, 1, 1)
) as rn
from trainingdays td cross join
(select @rn := 0, @i := NULL) vars
where number_of_pushups >= 100
order by id_user, date
) td
) td
group by grp
) td;
Your app can then check the value against whatever minimum you like.
Note: this assumes that there is only one record per day. The above can easily be modified if you are looking for the sum of the number of pushups on each day.