If a two-tailed test shows significance and the mean is higher, can you infer that one condition is significantly higher? Condition A has M=5, SD=1
Condition B has M=10, SD=1  

If a two-tailed test gives p&lt;.05, can you infer that Condition B was significantly higher than Condition A without conducting a one-tailed test?
Yes.

A two-tailed test simply corrects for the appropriate probability of observing a difference as large as you observe given the null hypothesis is true. This probability is twice the one-tailed probability (in effect, a two-tailed test with alpha=0.05 is the same as two one-tailed tests each with alpha=0.025). You do not need a one-tailed test to infer the direction. If there is a significant difference with a two-tailed test, it clearly must be in the direction of the observed difference.