First off, the rule of 4 slightly over-estimates with more than 10 outs. 11 outs it actually 42%.

If you just consider the 5, which comes 13% of the time. An A will come 6% of the time (3 outs, one chance), plus if a non-diamond 3 or 8 comes you split the pot (about 1%).

As a rule of thumb you can't count the 5s as an out at the table. You may already be behind an overpair, if not the 5 could be counterfeited. Plus, would you really be happy investing more money with Q5 on a 4567 board? If you knew villain had missed overs I would count the 3 fives as 1/2 out each.

What you should take from this is identifying live outs. That's more important than worrying about the exact odds in a given specific matchup where you already know both hands (which never happens in practice).