The F-contrast  is undirected, the t-contrast in SPM are always directed = one-sided. In your case with a single group the two tests produce equivalent results, with F = T^2.
If you just set up one one-sided t-contrast (e.g. ) because you're only interested in this direction, thresholded at a certain alpha, you will indeed get more significant findings than with one F-contrast. This is nothing surprising though. The F-contrast  thresholded at alpha is equivalent to two one-sided t-contrasts  and [-1] thresholded at alpha/2 each. Or put it differently, if you conduct two one-sided t-contrasts  and [-1] thresholded at alpha each, this would be equivalent to an F-contrast thresholded at alpha*2.
In neuroscience it is very common to look at both directions but to threshold the t-contrasts at .001 each, thus not accounting for no. of tests. This is sometimes interpreted as the t-contrast to be more sensitive, but actually it's due to not accounting for no. of performed tests.
Concerning your results, given that you only have five subjects there might just be too much variance to detect a consistent response / significant clusters/voxels, even if all subjects show a response going into the same direction. There might of course be other issues (outliers, noise, ...).