Both MT4 and MT5 Force index Calculation is Wrong.
Here's the formula in the Official MetaTrader CodeBase:
FORCE INDEX (i) = VOLUME (i) * ((MA (ApPRICE, N, i) - MA (ApPRICE, N, i-1))
MetaTrader Developers used first the moving average to smooth the current close and previous close instead of "Raw Form" of Force Index: "Current Volume * (Current Close - Previous Close)"..
The Default setting in MetaTrader Force Index is SMA even I changed that to EMA the signal is a little bit different compared to real formula of Force Index because they used the moving average first on the closing price instead of Raw form of Force index.. I tested this multiple times using my custom indicator to use the real formula of Force Index, and compare this other trading platform. In TradingView they used the exact formula of Elder's Force Index.
The real formula of Force Index according to Alexander Elders the Inventor of Force Index:
Force Index = Current Volume * (Current Close - Previous Close)
EFI = 13-day EMA of Force Index
The real calculation of force index uses "Exponential Moving Average" after we calculate the "Raw form of Force Index":
EMA((Volume today * (Close today - Close yesterday)), 13-period)
Based upon the real formulae you supplied, and @whroeder1's answer, I threw together this MQL5 version of Force Index, and all before my second cup of coffee.
Let me know if it displays what you expect from the true Force Index.