We conduct a comparative analysis of the original $\text{CoVaR}^=_{\alpha, \beta}(Y|X)$ and modified $\text{CoVaR}_{\alpha, \beta}(Y|X)$ measures of Conditional Value-at-Risk (CoVaR) using high-frequency returns of Bitcoin (BTC), Ethereum (ETH), Ripple (XRP), Solana (SOL), and Binance Coin (BNB) at 5-minute intervals. Additionally, we employ the Kolmogorov-Smirnov (KS) bootstrapping test to assess potential interdependencies among cryptocurrency returns. Our results indicate that, on average, estimates derived from CoVaR$_{\alpha,\beta}(Y|X)$ tend to surpass those from CoVaR$^{=}_{\alpha,\beta}(Y|X)$, with superior performance in the backtesting analysis. Moreover, the Kolmogorov-Smirnov (KS) test underscores a notable degree of interconnectedness within cryptocurrency returns.