Objectives: The present study examined the agreement and associations of the 5-time sit-to-stand (5STS) test, the countermovement jump test, and lower-limb muscle power equations with a set of physical performance tests in older adults. Methods: Five hundred and thirty-four community-dwelling older adults were recruited for the study. Lower-limb muscle power measures included 5STS, the countermovement jump test, and muscle power equations. Isometric handgrip strength, timed “up-and-go!”, the 6 min walking test, one-leg stand, and walking speed at usual and fast paces were used to assess physical performance. Pearson’s correlations and Bland–Altman analyses were conducted to examine associations among muscle power measures. Linear and multiple regressions were run to explore associations of 5STS, the countermovement jump test, and muscle power equations with physical performance tests. Results: Weak correlations were observed among lower-limb muscle power measures. Bland–Altman results indicated important differences among the countermovement jump test, 5STS, and muscle power equations. Results of multiple linear regressions indicated that 5STS, the countermovement jump test, and muscle power equations were significantly associated with measures of muscle strength and mobility. However, only 5STS was significantly associated with balance. Conclusions: Our results indicate that the performance on the countermovement jump test and 5STS is weakly correlated with lower-limb muscle power equations. The only exception was the correlation found between the countermovement jump test and relative muscle power, highlighting the importance of accounting for body mass in muscle power evaluations. Muscle power measures were similarly associated with performance on handgrip strength, timed “up-and-go!”, and the 6 min walking test. The exclusive association of 5STS with balance suggests that a reassessment of 5STS muscle power equations may be warranted.