Translation:Please talk slowly.
遅い has a negative or neutral feeling. Like のろのろ. It carries a feeling of laziness or dumbness. Or it just means slow as opposed to fast.
ゆっくり has a positive feeling. It means slow down, relax, take it easy. I has a feeling of gentleness and kindness, being careful and mindful.
If it is the verb 話す (はなす) then, when conjugated, the okurigana is always necessary. You will always conjugate it as 話します or 話して. If you are using the noun 話(はなし) then the okurigana is not necessary. For example: その話を聞きました (I listened to the speech). If people are speaking more formally they will frequently say something along the lines of 彼はお話をしました (He gave a talk)
There seems to be some confusion in the forum about おそく「遅く、遅い」vs ゆっくり
Although often times the two words seem to be related and translated both to "slow; slowly", the usage is different
I have never heard anyone say 遅く話して。( that is just my experience; perhaps a situation exists? ) And for the meaning of "Speak slowly", Duo is correct with ゆっくり話して
Now for 遅い:
The train is late.
The train is ( running ) slowly.
You can make the speed more clear with 電車の速度「そくど」が
This is just the natural condition situation of the train
On the other hand,
The boy runs until it is late
The kid runs later in the day
The kid is slow. ( He is naturally a slow runner because he doesn't have the talent to run fast)
The kid runs slowly. ( This is an intentional action with ゆっくり, the kid can run much faster or even more slowly )
The train engineer runs the train slowly due to the strong winds.
The train engineer runs the train later in the day
Weight training later in the day and slowly is more effective
Don't fail me now Duo formatting!!!