Question 988618
The five consecutive dates are:
February 27, February 28, March 1, March 2, and March 3 of a year that is not a leap year.
Five consecutive days often will be in the same month and hence consecutively numbered, as in
{{{n-2}}} , {{{n-1}}} , {{{n}}} , {{{n+1}}} , and {{{n+2}}} , which add up to
{{{n-2+n-1+n+n+1+n+2=5n}}} , so the sum would be a multiple of 5.
Since {{{61}}} is not a multiple of 5,
the 5 consecutive days must include the end of a month and the beginning of the next month.
If the first month {{{30}}} or {{{31}}} days,
the possible sums do not add up to {{{61}}}  :
{{{30+31+1+2+3=67}}} , {{{31+1+2+3+4=41}}} ,
{{{29+30+1+2+3=65}}} , {{{30+1+2+3+4=40}}} .
So, the first month must be February, with {{{28}}} or {{{29}}} days.
Since {{{28+2=30}}} and {{{27+3=30}}},
the sum {{{27+28+1+2+3=61}}} works.
The other possibility with two days in February and three in March,
{{{29+28+1+2+3=63}}} , yields a sum that is too high,
and using only one day from February will yield too low a sum.