No, speaked is not a word. Speak is irregular: past tense spoke /spoʊk/, past participle spoken /ˈspoʊkən/. Try: I spoke to her yesterday or I have spoken to her already.
Using the forms
There was complete silence, nobody spoke. Here spoke /spoʊk/ does the past-tense work on its own, with no -ed ending attached.
He didn't like the words spoken at the meeting. This is the participial use: spoken /ˈspoʊkən/ follows another verb or describes something done, as with words spoken.
A useful past-participle pattern: I have spoken to her already. The second vowel reduces in speech, so /ˈspoʊkən/ sounds lighter on the final syllable than the stressed /spoʊk/ of spoke.
Quick check: choose spoke or spoken for She has ___ to the manager twice. The right answer is spoken, because has needs the past participle. If you picked spoke, remember that simple spoke never follows have or has.